Questions from General Calculus

Q: (a) Graph the function. (b) Use

(a) Graph the function. (b) Use l’Hospital’s Rule to explain the behavior as x ( 0. (c) Estimate the minimum value and intervals of concavity. Then use calculus to find the exact values. f(x) = x2 ln...

Q: (a) Graph the function. (b) Use

(a) Graph the function. (b) Use l’Hospital’s Rule to explain the behavior as x ( 0. (c) Estimate the minimum value and intervals of concavity. Then use calculus to find the exact values. f(x) = x e1/x...

Q: If f is the function considered in Example 3, use a

If f is the function considered in Example 3, use a computer algebra system to calculate f ‘ and then graph it to confirm that all the maximum and minimum values are as given in the...

Q: Prove Fermat’s Theorem for the case in which f has a local

Prove Fermat’s Theorem for the case in which f has a local minimum at c.

Q: A cubic function is a polynomial of degree 3; that is

A cubic function is a polynomial of degree 3; that is, it has the form f (x) = ax3 + bx2 + cx + d, where a ≠ 0. (a) Show that a cubic function can have two, one, or no critical number(s). Give example...

Q: Explain the difference between an absolute minimum and a local minimum.

Explain the difference between an absolute minimum and a local minimum.

Q: Suppose f is a continuous function defined on a closed interval [

Suppose f is a continuous function defined on a closed interval [a, b]. (a) What theorem guarantees the existence of an absolute maximum value and an absolute minimum value for f ? (b) What steps woul...

Q: For each of the numbers a, b, c, d

For each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum.

Q: For each of the numbers a, b, c, d

For each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum.

Q: Find the derivative of the function. Simplify where possible.

Find the derivative of the function. Simplify where possible. R(t) = arcsin(1/t)