NZ Level 7 (NZC) Level 2 (NCEA)
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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
Approx 5 minutes
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Consider the function $f\left(x\right)=x^2+3x+4$f(x)=x2+3x+4.

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

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

Outcomes

M7-10

Apply differentiation and anti-differentiation techniques to polynomials

91262

Apply calculus methods in solving problems

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