11. Differentiation
Standard Level
11.13 Graphing techniques using calculus
Interactive practice questions
Consider the function $f\left(x\right)=2x^3-12x^2+18x+3$f(x)=2x3−12x2+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$0≤x≤7.
g
State the absolute minimum value of the function within the range $0\le x\le7$0≤x≤7.
Medium
10min
Consider the equation $y=9x^2+18x-16$y=9x2+18x−16.
Medium
8min
Consider the equation $y=-x^2+8x-21$y=−x2+8x−21 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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