The function $f (x) = (x - 3)^{2}$ satisfies all the conditions of mean value theorem in [3, 4]. A point on $y = (x - 3)^{2},$ where the tangent is parallel to the chord joining (3, 0) and (4, 1) is

(\frac{7}{2}, \frac{1}{2})

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(\frac{7}{2}, \frac{1}{4})

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(1, 4)

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(4, 1)

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Solution

The correct option is B $(\frac{7}{2}, \frac{1}{4})$
Slope of the chord joining (3, 0) and (4, 1) = $\frac{1 - 0}{4 - 3}$ = 1
Slope of the tangent at any point on the given curve -
f'(x) = 2.(x-3)
So, 2(x-3) = 1
or x = $\frac{7}{2}$
Therefore the point will be = (7/2, 1/4)

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Q. The function

f (x) = (x - 3)^{2}

satisfies all the conditions of mean value theorem in [3, 4]. A point on

y = (x - 3)^{2},

where the tangent is parallel to the chord joining (3, 0) and (4, 1) is

Q. The function

f (x) = (x - 3)^{2}

satisfies all the conditions of mean value theorem in [3, 4]. A point on

y = (x - 3)^{2},

where the tangent is parallel to the chord joining (3, 0) and (4, 1) is

The function $f (x) = {(x - 3)}^{2}$ satisfies all the conditions of the mean value theorem in $[3, 4] .$ A point on $y = {(x - 3)}^{2}$ , where the tangent is parallel to the chord joining $(3, 0)$ and $(4, 1)$ is

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The function f(x)=(x−3)2 satisfies all the conditions of mean value theorem in [3, 4]. A point on y=(x−3)2, where the tangent is parallel to the chord joining (3, 0) and (4, 1) is

The correct option is B (72,14)Slope of the chord joining (3, 0) and (4, 1) = 1−04−3 = 1 Slope of the tangent at any point on the given curve - f'(x) = 2.(x-3) So, 2(x-3) = 1 or x = 72 Therefore the point will be = (7/2, 1/4)

The function $f (x) = (x - 3)^{2}$ satisfies all the conditions of mean value theorem in [3, 4]. A point on $y = (x - 3)^{2},$ where the tangent is parallel to the chord joining (3, 0) and (4, 1) is

The correct option is B $(\frac{7}{2}, \frac{1}{4})$
Slope of the chord joining (3, 0) and (4, 1) = $\frac{1 - 0}{4 - 3}$ = 1
Slope of the tangent at any point on the given curve -
f'(x) = 2.(x-3)
So, 2(x-3) = 1
or x = $\frac{7}{2}$
Therefore the point will be = (7/2, 1/4)