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4.04 Graphing techniques using calculus

Interactive practice questions

Consider the function $f\left(x\right)=2x^3-12x^2+18x+3$f(x)=2x312x2+18x+3.

a

Solve for the $x$x-coordinates of the turning points of the function.

b

Determine $f''\left(1\right)$f(1).

c

Determine $f''\left(3\right)$f(3).

d

State the coordinates of the local maximum.

e

State the coordinates of the local minimum.

f

State the absolute maximum value of the function within the range $0\le x\le7$0x7.

g

State the absolute minimum value of the function within the range $0\le x\le7$0x7.

Medium
10min

Consider the equation $y=9x^2+18x-16$y=9x2+18x16.

Medium
8min

Consider the equation $y=-x^2+8x-21$y=x2+8x21 over the domain $\left[0,6\right]$[0,6].

Medium
4min

Consider the equation $y=2\left(x+5\right)^3+3$y=2(x+5)3+3.

Medium
6min
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Outcomes

MA12-3

applies calculus techniques to model and solve problems

MA12-6

applies appropriate differentiation methods to solve problems

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