Calc Review for Quiz 5. 2nd Sem. Absolute Extrema& Rolle's Theo

Use the diagram to classify relative and absolute extrema.

Select ALL that apply.

Find all the critical numbers of

f(x) = 3x⁴ – 8x³ – 90x² + 700.

Select ALL that apply

Find the absolute extrema of $$f\left(x\right)=-3x^2+30x+6$$ on the closed interval [ 2, 9].  Select ALL the correct answers.  (Feel Free to use Desmos Graphing Tool)

Find the absolute extrema of   $$f\left(x\right)=x^3-3x^2-24x+4$$  on the closed 

interval [ -7, 6].   Select ALL the correct answers.   (Feel Free to use Desmos Graphing Tool)

Find the absolute extrema of   $$f\left(x\right)=-5x+3$$  on the closed interval [ -2, 4].   Select ALL the correct answers.  (Feel Free to use Desmos Graphing Tool)

Find the two x - intercepts of  f(x) = x² + 4x - 77,  and then find x that verifies  Rolle’s Theorem within the intercept.

$$f\left(x\right)=4x^2-3x,\$$   Using Rolle's Theorem is there a value of c such that f'(c)=0 in the interval $$\left[1,3\right]$$ and if so what is this value of c?

$$f\left(x\right)=2x^2+6x+8$$   Using Rolle's Theorem is there a value of c such that

f ' (c)=0 in $$\left[-3,0\right]$$  and if so what is this value of c?

$$f\left(x\right)=\frac{x^2}{8x-15},\ \left[3,5\right]\$$   Using Rolle's Theorem is there a value of c such that

f ' (c)=0 and if so what is this value of c?

Find the x in $$\left[\frac{5\pi}{4},\ \frac{7\pi}{4}\right]$$  that satisfies Rolle's theorem in f(x) = 18sinx

Select ALL that apply.