Question

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

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Limits

Functions

Continuity

Applications of Derivative

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: convert the indefinite integral into definate integral using the interval [0,1]

A: Click to see the answer

Q: E. Sketch the graph of an example of a single function f such that all of the following hold: F(1) =...

A: f(1)=3 means (1,3) is a point  means f(x) goes downwards on the left side  means the graph goes up...

Q: The irst 1our terfns ol a sequence are given. mine whetner these terms Can be the terms of a geometr...

A: Click to see the answer

Q: Calculus 3 Question:   Section 13.1

A: Click to see the answer

Q: Find the volume of the solid generated by revolving the region bounded by y=x+3, y=4 and x=5 about t...

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the bla...

Q: Calculus Question

A: Click to see the answer

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative  

Q: ConTerpes Comparišon Test. Determine it the followig serves p The direst Show the work! or oliverpes...

A: Click to see the answer

Q: Complete the table by computing f(x) at the given values of x. (Round your answers to three decimal ...

A: Click to see the answer

Q: The table gives the values of a function obtained from anexperiment. Use them to estimate ∫93f(x) dx...

A: Click to see the answer

Q: QUICK CHECK 3 Show that 1 V = 5 (y² – x²) is a stream 2 function for the vector field F = (y, x). Sh...

A: Click to see the answer

Q: graph the following  a) y=2 cos x b) y=cos2x c)y=2sinx d) y=sin2x

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Find all the x-values at which the critical points occur of the function f(x) = 5x³ – 16x2 + 11x on ...

A: Click to see the answer

Q: On a sunny​ day, a tree and its shadow from the sides of a right triangle. If the hypotenuse is 35 m...

A: Click to see the answer

Q: Express the vectors in Exercises 9–12 in terms of their lengths and directions.

A: Q(9).  Given:  First find the length and then direction. Find magnitude. Find the direction of gi...

Q: Solve:[(6/x + 3) - (5/x - 2)] =(-20/x2 + x - 6)

A: Click to see the answer

Q: Calculate the sum of these convergent infinite series. n 3 Σ8 4 4 Σ а. b. in(n +2) n=0 n=1 N| 8.

A:  

Q: Evaluate each integral by interpreting it in terms of areas.

A:  

Q: Let r, = 1,i+yj+zjk, r2 = z,i+ aj + zak and r = zại + nj+zak be the position vectors of points A(z1,...

A: Click to see the answer

Q: A table of values of an increasing function  f is shown. Usethe table to find lower and upper estima...

A: Click to see the answer

Q: (a) Va? – x² dx .2 - (Ъ) V1 – x² dx

A: (a) The given Integral is It can be written as          

Q: Show that

A:  

Q: For the following exercises, use the given values to find (f-')' (a).

A: Click to see the answer

Q: The figure shows the graph of a function  f. Suppose thatNewton’s method is used to approximate the ...

A: Click to see the answer

Q: Assume C is a circle centered at the origin, oriented counterclockwise, that encloses disk R in the ...

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want an...

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given conditio...

A: Click to see the answer

Q: sin z Show that

A:  

Q: 1

A: Click to see the answer

Q: 8

A: Click to see the answer

Q: use the following to solve the right triangle. Give angles in degrees and minutes. Round the missing...

A: Click to see the answer

Q: Solve the initial value problem dy/dx=2/x+1, y(0)=2.

A: Click to see the answer

Q: Evaluate the indefinite integral 5e^5x*sin(e^5x) *dx

A: Click to see the answer

Q: The total stopping distance T of a vehicle is T = 2.5x + 0.5x2 where T is in feet and x is the speed...

A: Click to see the answer

Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 In(cos(t)) k, osts n/4

A: Given:

Q: Evaluate the integral ∫dx / √x+1.

A:  

Q: help me please Evaluate the upper and lower sums for f (x) = 2 + sin (x), 0 ≤ x ≤ π, with n = 2, 4, ...

A: Click to see the answer

Q: Find the measure​ (in radians) of a central angle of a sector of area 53 square inches in a circle o...

A:  

Q: Use a linear approximation (or differentials) to estimate the given number. Consider the linear appr...

A: Click to see the answer

Q: p = -x2 - 2x + 86 and p = 8x + 11 equilibrium quantity thousand units equilibrium price dollars

A: Click to see the answer

Q: Let | f(x) dr = 9, f(x) dr = –2, g(x) dx = 15, g(x) dx = 5, Use these values to evaluate the given d...

A: Click to see the answer

Q: Find two positive numbers that satisfy the given requirements. The sum of the first number and twice...

A: Let the numbers are x and y So, x+2y=108  Or, x= 108-2y    Product of them = P=  xy= (108-2y)y