Question

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)
f(x) = x^3 − 4x^2 − 16x + 9, [−4, 4]
Find c=

Answer 1

Step-by-step explanation:

$\qquad\sf {:}\longrightarrow f (-4)=(-4)^3-4 (-4)^2-16 (-4)+9$

$\qquad\sf {:}\longrightarrow -64-64+64+9$

$\qquad\sf {:}\longrightarrow -64+9$

$\qquad\sf {:}\longrightarrow -55$

Answer 2

Step-by-step explanation:

$\bf \: given \: that \\ \bf \: f(x) = {x}^{3} - {4x}^{2} - 16x + 9 \\ \\ \tt {:}\longrightarrow f( - 4) = { - 4}^{3} - 4( - 4) {}^{2} - 16( - 4) + 9 \\ \tt {:}\longrightarrow - 64 - 4(16) + 64 + 9 \\ \tt {:}\longrightarrow - 64 + 9 \\ \tt {:}\longrightarrow - 55$