Question

3. Recall that critical points occur where $f'(x) = 0$ or where $f'(x)$ is undefined. Let $f(x) = x + a\sqrt{x}$ where $a$ is some positive constant. (a) Set $f'(x) = 0$. Show why this can't happen. (b) What is the only critical point of $f(x)$? (c) Show that $f$ will always be increasing for $x > 0$. (d) Show that $f$ will always be concave down for $x > 0$.

          3.
Recall that critical points occur where $f'(x) = 0$ or where $f'(x)$ is undefined. Let
$f(x) = x + a\sqrt{x}$
where $a$ is some positive constant.
(a) Set $f'(x) = 0$. Show why this can't happen.
(b) What is the only critical point of $f(x)$?
(c) Show that $f$ will always be increasing for $x > 0$.
(d) Show that $f$ will always be concave down for $x > 0$.

3.
Recall that critical points occur where f'(x) = 0 or where f'(x) is undefined. Let
f(x) = x + a√(x)
where a is some positive constant.
(a) Set f'(x) = 0. Show why this can't happen.
(b) What is the only critical point of f(x)?
(c) Show that f will always be increasing for x > 0.
(d) Show that f will always be concave down for x > 0.

Added by Catalina L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/07/2023

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The derivative of f(x) is f'(x) = 1 + a. Show more…

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3. Recall that critical points occur where f=0 or where f is undefined. Let f(x) = x + ax where a is some positive constant. a) Set f'(x) = 0. Show why this can't happen. b) What is the only critical point of f? c) Show that f will always be increasing for x > 0. d) Show that f will always be concave down for x > 0.