# Graphical Interpretation of Differentiability

## Trending Questions

**Q.**

What is the use of graphs?

**Q.**

What is the parabolic curve?

**Q.**Let f′(x)=192x32+sin4πx for all x∈R with f(12)=0. If m≤1∫12f(x) dx≤M, then the possible values of m and M are

- m=13, M=24
- m=14, M=12
- m=−11, M=0
- m=1, M=12

**Q.**Let S be the set of all points in (−π, π) at which the function, f(x) = min {sinx, cosx} is not differentiable. Then S is a subset of which of the following?

- {−3π4, −π4, 3π4, π4}
- {−π2, −π4, π4, π2}
- {−3π4, −π2, π2, 3π4}
- {−π4, 0, π4}

**Q.**Consider the function f(x)=x34−sinπx+3

- f(x) does not attain value within the interval [−2, 2]
- f(x) takes on the value 213 in the interval [−2, 2]
- f(x) takes on the value 314 in the interval [−2, 2]
- f(x) takes no value p, 1<p<5 in the interval [−2, 2]

**Q.**Let f:(−1, 1)→R be a function defined by f(x)=max{−|x|, −√1−x2}. If K be the set of all points at which f is not differentiable, then K has exactly

- one element
- two elements
- three elements
- five elements

**Q.**

If $g\left(x\right)$ is a polynomial satisfying $g\left(x\right)g\left(y\right)=g\left(x\right)+g\left(y\right)+g\left(xy\right)-2$ for all real $x$ and $y$ and $g\left(2\right)=5$, then $\underset{x\to 3}{\mathrm{lim}}g\left(x\right)=$

$9$

$10$

$25$

$20$

**Q.**

How do you tell if a parabola opens left or right$?$

**Q.**What is the perfect graph for action potential.?

**Q.**Which of the following curve(s) is(are) symmetric about y=x?

- x2−y2=16
- x2+y2=16
- xy=16
- 3x2+4y2=12

**Q.**

The horizontal asymptote of the curve y=e1x is

- y=0
- y=1
- y=−1
- y=2

**Q.**If f(x) is a differentiable everywhere then

- |f(x)| is differentiable everywhere
- |f|2 is differentiable everywhere
- f|f| is not differentiable at some point
- None of these

**Q.**

Select the correct statement for the function $f\left(x\right)=x{e}^{1-x}$.

Strictly increases in the interval $\left(\frac{1}{2},2\right)$

Increases in the interval $\left(0,\infty \right)$

Decreases in the interval $\left(0,2\right)$

Strictly decreases in the interval $\left(1,\infty \right)$

**Q.**Which of the following curve has no asymptote:

- y=5x
- y=logex
- y=x2−3x+2
- x2−4y2=4

**Q.**Give an example of a function which is continuous everywhere but not differentiable at a point.

**Q.**f(x)=min{cosx, 1−sinx}, −π≤x≤π. Then which among the following options is/are correct

- f(x) is not differentiable at x=0
- f(x) is differentiable at x=π2
- f(x) is discontinuous at x=0
- f(x) is continuous at x=π2

**Q.**Let f(x)={max{ex, e−x, 2}, x≤0min{ex, e−x, 2}, x>0.

Which of the following statements is (are) CORRECT?

- f(x) is discontinuous at x=0.
- f(x) is non-differentiable at exactly two points.
- f(x) has non-removable type of discontinuity at x=0 with jump of discontinuity equal to 2.
- f(x) is continuous but non-differentiable at x=ln12.

**Q.**The area of the region (x, y) : xy≤8, 1≤y≤x2 is

- 16log2e−143
- 8log2e−143
- 16log2e− 6
- 8log2e−73

**Q.**Let f:R→R be twice continuously differentiable. Let f(0)=f(1)=f′(0)=0. Then

- f′′(x)≠0 for all x
- f′′(c)=0 for some c∈R
- f′′(x)≠0 if x≠0
- f′(x)>0 for all x

**Q.**Let f:R→R be a function defined by f(x)=max{x, x3}. Then the set of all points where f is not differentiable, is

- {−1, 0}
- {−1, 0, 1}
- {0, 1}
- {−1, 1}

**Q.**The number of intersection points of the function f(x)=sinx & y=0.5 in

(a). x∈ (0, 3π)

(b). x∈[−6π, 6π] respectively are:

- 6, 10
- 4, 10
- 4, 12
- 6, 12

**Q.**The motion of a body is given by equation dv/dt=a-bv. The velocity of particle varies with time as. Draw the graph.

**Q.**If f(x)=sin−1(cosx)cos−1(sinx) ∀x∈[0, 2π], then the number of point(s) of non differentiability is

- 0
- 1
- 3
- 4

**Q.**What is the nature of the graph: y=2x2

- parabola passing through origin
- Hyperbola but not passing through origin
- Hyperbola passing through origin
- ellipse passing through origin

**Q.**

Determine if the graph is symmetric about the $x$-axis, the $y$-axis, or the origin.$\mathrm{r}=4\mathrm{cos}3\mathrm{\theta}$.

**Q.**Let f(x) be a polynomial function satisfying the following conditions

limx→∞f(x)|x|3=0, limx→∞(√f(x)−x)=−1 and f(0)=0

(where, [.] denotes greatest integer function) then which of the following is/are correct?

- The number of points of discontinuity of g(x)=[f(x)] in [0, 3] is 3
- The number of points of discontinuity of g(x)=[f(x)] in [0, 3] is 5
- The number of points of non-derivability of h(x)=∣∣f(|x|)∣∣ is 4
- The number of points of non-derivability of h(x)=∣∣f(|x|)∣∣ is 3

**Q.**If f(x)=⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩x2+2, x<0−2e−x, 0≤x<2, −2e2(x−3), x≥2 then

- |f(x)| is discontinuous at 0 points
- |f(x)| is discontinuous at 2 points
- |f(x)| is not differentiable at 2 points
- |f(x)| is not differentiable at 3 points

**Q.**

Use the method of symmetry to find the extreme value of each quadratic function and the value of $x$ for which it occurs. $g\left(x\right)=(5-x)(2x+3)$ pls give it in this form:

The $x$-intercepts of the graph of the function are (_, _), (_, _). The midpoint of the $x$-intercepts is ___. The extreme value is (a maximum or a minimum).

$g\left(\right)$=_____

**Q.**Assertion :Let function f:R→R is such that f(x)f(y)−f(xy)=x+y for all x, y∈R

f(x) is a Bijective function. Reason: f(x) is a linear function.

- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- Assertion is correct but Reason is incorrect
- Assertion is incorrect but Reason is correct

**Q.**What is the nature of the graph : y=−4x2+6

- Hyperbola not passing through origin
- Ellipse not passing through origin
- it is not a conic
- parabola not passing through origin