Give an example showing that, even if f 0 (c) = 0, it could happen that f(x) does not have a local maximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?

Q: In the function:  f(x)=(12−3x)e^x  What are the critical numbers of the function?  When is the…

A:

Q: Find a cubic function f(x)  = ax3 + bx2 +cx +d thathas a local maximum value of 3 at x =-2 and a…

A: At x=-2 , y=3  So,  at x=1, y=0

Q: 2. Find the absolute maximum and absolute minimum value of f(x) = 6x – x on [1, 7].

A: Given function fx=6x-x2 To find the absolute maximum and minimum first find critical values.…

Q: f(x) = 2x² - e²

A:

Q: FIND THE MINIMUM AND MAXIMUM VALUE F (X) = X/(1-X) X e(0,1)

A:

Q: consider the function f(x)= xe-4x,t) , 0≤x≤2. and an absolute maximum value equal to:  which is…

A: Given: fx=xe-4x, 0≤x≤2

Q: Prove that Pr (|X − a| < τ ) takes its maximum value when a = µ where X ~ N (µ, σ2)

A:

Q: On the graph of f(x) = cos x and the interval [27, 47), for what value of x does f(x) achieve a…

A: Here given function

Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: Find the points at which y=f(x)=4x−ln(2x)y=f(x)=4x−ln⁡(2x) has a global maximum, a global minimum,…

A: Given function

Q: Find the absolute maximum and minimum values of ƒ(x) = ex - 2x on [0, 1] .

A: Consider the given function.

Q: (b) Let f(x) = 12x35+ 15x* – 40x³ + 17. Find the critical numbers, and show what the Second…

A: f(x) = (12x 5+15x4 -40x3 +17.   critical points   f'(x) = 0   60 x4 + 60x³-120x²  = 0.   x² ( 60…

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

A:

Q: Give an example that: the function f has a local maximum at x = 1/2, but it is not differen- tiable…

A: Consider the function:

Q: Determine the values of constants a, b, c, and d so that ƒ(x) = ax3 + bx2 + cx + d has a local…

A:

Q: Find the absolute maximum and absolute minimum of h(x) = x/e^x on [0,4]

A:

Q: ) Because f(-1) and f' changes from negative to positive at x = f(-1) = -7e-1 is a local (and…

A:

Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

Q: 4. If f has a local minimum at x = 0 and a local maximum at x – 2, what can you say about f'(0) and…

A: f has a local minimum at x=0 and a local maximum at x=2.

Q: Consider the function f(x) = z over the interval (-2, 2). Does the extreme value theorem guarantee…

A:

Q: What is the absolute minimum value of g(x)=−2x^2−2x−1 over [−3,4]?

A:

Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

Q: 2. ts): Find the absolute maximum / minimum values of the function f(x) = x(6-x) over the interval…

A:

Q: 2. Suppose that f (a, b) is an absolute maximum of the function f(x, y). Must f (a, b) also be a…

A:

Q: for the funciton f(x) = x^3 - 75x Its local maximum  is____, which occurs at _____> Its local…

A:

Q: If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f'(0) and…

A:

Q: Find a cubic function f(x) = ax + bx2 + cx + d that has a local maximum value of 4 at x = -3 and a…

A: Here we have to find the cubic function that has a local maximum value of 4 at x= -3 and a local…

Q: On the graph of f(x) = sin x and the interval [27, 47), for what value of x does f(x) achieve a…

A:

Q: While studying for Test 2, Miguel says to his classmates "Fermat's Theorem (page 5 in Lecture Notes…

A: According to Miguel's statement Fermat's theorem is " For a function f(x), if f'(x)=0, then f has…

Q: Find the values of constants a, b, and c so that the graph of y = ax + bax2 + cx has a local maximum…

A:

Q: Find the absolute maximum value of p(x) = -x² – x + 1 over er[-1,1].

A:

Q: Find the value of x at which the absolute minimum occurs (if it exists) for the function f(x) = -x2…

A:

Q: Find constants a and b in the function f(x): ar In(x) such that f() = 1 and the function function…

A:

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a. a local maximum at x = -1 and a local…

A: Find first derivative.

Q: Given the function y"=-6X(x²-ax+4) (x+a)³ (x -1)³ 3. with (X+2)(x-) - analysiS Enclude all maximums…

A: given that y=-x3x+2x-2find the maxima and minima for the given function

Q: Find the points at which y=f(x)=4x−ln(2x) has a global maximum, a global minimum, and a local,…

A:

Q: Discuss the extreme-value behavior of the function ƒ(x) = x sin (1/x), x ≠ 0. How many critical…

A: Given fx=xsin1x,x≠0

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −4 and a…

A:

Q: snip

A: Given:                          fx=x+1x Differentiate f(x) with respect to x…

Q: If f'(x)=x^3-2x^2-x+2, then f has a relative minimum at x=

A: If f'(x)=x3-2x2-x+2, then f has relative minimum at x

Q: Find the absolute maximum and minimum values of f(x) = (x² + x)i over the interval [-3, 4]. absolute…

A:

Q: 2) Find the absolute minimum value on (0,∞ ) for 4 f(x)= 5+x+

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local maximum at x = -1 and a local minimum…

A: Given: fx=x3+ax2+bx To find a, b such that function has local maxima at x = -1 and local minima x =…

Q: 2. Consider a function f : R → R where S(x) = x³ – 3x for all æ e R. Identify all critical points…

A: Given the function fx=x3-3x  ,x∈R. To find the critical points and the local maximum and local…

Q: Where are there local minimum(s)/maximum(s) f(x)=3(2x-1) -4(x+1)?

A:

Q: 2. Give an example of a function f: (0, 00) → K that is continuous and bounded but does not achieve…

A: It is an usual example which derivative not vanish anywhere

Q: Find the absolute maximum of h(x)=x2 −x−2 over [−3,6]. Enter only the y-coordinate of the maximum.

A: Determine the  derivative of the function  and find the critical points.