Question

3. Find the absolute minimum and the absolute maximum of the following functions on the given interval. (a) $f(x) = 4x^3 - x^4$ on $[-1, 5]$. (b) $g(t) = t^{-2} ln(t)$ on $[1/2, 4]$. 4. Consider the function $f(x) = x^2 - 4x + 8$ on the interval $[0, 4]$. (a) Verify that this function satisfies the three hypotheses of Rolle's Theorem on the interval. (b) By the Rolle's theorem, there exists at least one value $c$ such that $f'(c) = 0$. Find all such values c.

          3. Find the absolute minimum and the absolute maximum of the following functions on the given
interval.
(a) $f(x) = 4x^3 - x^4$ on $[-1, 5]$.
(b) $g(t) = t^{-2} ln(t)$ on $[1/2, 4]$.
4. Consider the function $f(x) = x^2 - 4x + 8$ on the interval $[0, 4]$.
(a) Verify that this function satisfies the three hypotheses of Rolle's Theorem on the interval.
(b) By the Rolle's theorem, there exists at least one value $c$ such that $f'(c) = 0$. Find all such values
c.

3. Find the absolute minimum and the absolute maximum of the following functions on the given
interval.
(a) f(x) = 4x^3 - x^4 on [-1, 5].
(b) g(t) = t^-2 ln(t) on [1/2, 4].
4. Consider the function f(x) = x^2 - 4x + 8 on the interval [0, 4].
(a) Verify that this function satisfies the three hypotheses of Rolle's Theorem on the interval.
(b) By the Rolle's theorem, there exists at least one value c such that f'(c) = 0. Find all such values
c.

Added by Teresa B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Aman Gupta

Step 1

(a) To verify that the function f(x) = 4x + 8 satisfies the three hypotheses of Rolle's Theorem on the interval [0,4], we need to check the following: Show more…

Show all steps

Thanks for your feedback!

Find the absolute minimum and the absolute maximum of the following functions on the given interval: f(x) = 4x^3 - x^4 on [-1, 5]. (b) g(t) = t^{-2} ln(t) on [1/2, 4]. Consider the function f(x) = x^2 - 4x + 8 on the interval [0, 4]. (a) Verify that this function satisfies the three hypotheses of Rolle's Theorem on the interval. (b) By the Rolle's theorem, there exists at least one value c such that f'(c) = 0. Find all such values c.