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India
Class XI

Rate of change functions

Interactive practice questions

Consider the function $f\left(x\right)=7-x^2$f(x)=7x2.

a

Find an expression for the derivative $f'\left(x\right)$f(x) using first principles.

Show all steps of working.

b

Hence calculate the gradient of $f\left(x\right)$f(x) at the point where $x=-1$x=1.

Easy
5min

Consider the function $f\left(x\right)=x^2+3x+4$f(x)=x2+3x+4.

Easy
5min

Consider the function $f\left(x\right)=x^3$f(x)=x3.

Easy
5min

Consider the function $f\left(x\right)=x^4$f(x)=x4.

Medium
5min
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Outcomes

11.C.LD.1

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

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