Differentiation measures how fast the function is changing with respect to the change in independent variable.

True

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False

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Solution

The correct option is A True
As discussed in the video the derivative of a function at a point gives the instantaneous rate of change of the function at that point. Graphically it would mean that a curve whose derivative is numerically higher will be steeper at that point than a curve with numerically lower derivative value. And a steeper graph means that its value is changing more quickly with change in independent variable than the one which is less steep.
Here please note that while comparing the derivative values for steepness, please compare their modulus only. For example the curve with a derivate value of -5 will be steeper than the curve with a derivative value of 2. So the modulus of the derivative is what we are concerned with in such cases.

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Similar questions

A strong correlation between the dependent and the independent variable suggests that the change in the independent variable is caused by the change in the dependent variable. State true or false.

Q. Differentiation gives us the instantaneous rate of change of one variable with respect to another.

Q. Write True or False with a reason.
Price elasticity of supply measures the change in quantity supplied in response to a change in own price of the commodity.

Q. If the independent variable

x

is changed to

y

, then the differential equation

x \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{3} - (\frac{d y}{d x}) = 0

is changed to

x \frac{d^{2} x}{d y^{2}} + {(\frac{d x}{d y})}^{2} = k

where

k

equals

Q. The changes in a function y and the independent variable x are related as

\frac{d y}{d x} = x^{2}

. Find y as a function of x.

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