6. Determine whether the given function is differentiable at the indicated point(s). (a) h(x) = x|x| at c = 0. (b) k(x) = |x|+ |x – 1| at c = 0 and c2 = 1.

Q: Find constants a and b in the function f(x) = axe“ such that fE) = 1 and the function has a local…

A: The given function is fx=axebx. It is given that f15=1. So, f15=a·15·eb·151=aeb55aeb5=5

Q: Let g (x) = f' (x) be a continuous function. If the derivative of the continuous function g (x)…

A: Explained below

Q: ´28 – e14z x 0 Determine whether the function f(x) = 14x – 1

A: Solution: Consider the given function is  f(x) = x8-e14x    x<014x-1       x≥0 To check whether…

Q: For the function y =f(x), it was found out that f"(c) = 0. What can be said that x=c? O critical…

A: We can find the answer as below.

Q: Find all critical points of the function. f(t) = t - √(t + 1)

A: The critical point of the function f(t)=t-t+1 is obtained by equating the first derivative of the…

Q: Q5: a- Use two segment trapezoidal rule to integrate the following function numerically: f(x) =…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 4. Find the extrema of the function f(x) = Vx (x + 1) and the intervals on which its graph is…

A:

Q: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

Q: Let ​h(x)=​f(g(x)), where f and g are differentiable on their domains. If ​g(−1​)=2 and g′​(−1​)=7​,…

A:

Q: let                    x^2+1   if x is less than 1 f(x)=                   x+1        if x is…

A: Consider the given function fx=x2+1  if x<1x+1   if x≥1. The point is x = 1. Obtain the left hand…

Q: The function f(x) = e + e has a relative extremum at Select one:

A:

Q: 6) Suppose f (x) is a differentiable function such that f (1) = 7 and f'(1) = 2. Use a tangent line…

A: This question is based on deduction of straight line using given information.

Q: (1) Where on the line r = ay does the function f(x, y) = (x – a)² + (y – 2)2 attain its smallest…

A: The line whose equation is of the form y=mx is passes through the origin and slope of the line is m.

Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

A:

Q: For the function y =f(x), it was found out that f(c) = 0. What can be said that x=c? O critical…

A:

Q: 1. Find the discontinuity point/s of f(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Let f(x) be a differentiable function for -3<x<1. Over this interval f(x) has exactly one critical…

A: for maxima or minima, we need to check second derivative of the function.

Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

A:

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

A:

Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

A:

Q: Let f be a differentiable function such that f(-1) = 10 and f' (x) = x – 2. What is the…

A:

Q: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

A:

Q: If f(x) =0 at x=c then f has either a minimum or maximum at x=c. If a differentiable function f has…

A: To Determine: true or false                           1) if f'(x)=0 at x=c then f has either a…

Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: 1. Show that function f(x)=D|x | is not differentiable at 0

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

A:

Q: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

A:

Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

A: First let us find the partial derivatives of the given function f(x,y)=x+y as shown below:…

Q: 1. Is a function f(x)=√x differentiable at a) X = 1 b) X = 0 c) X = -1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

A: Find the derivative for the function h(x). Now, the derivative for the function is the slope for the…

Q: 1(a): Find the value of k that makes function continuous at x = 4 4x +8 > 4 4x – k a <4 f(x) =

A:

Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: Q3) If the function (2x + 1 +2 x > h) XSh f(x) having limit at x = h. Find the value of h. Q4) f(x,…

A: Our objective is to solve the above questions.

Q: 3. Find a linear approximation to the function at the point x = 3. y = f(x) = x²e + 8x

A:

Q: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

A: We need to check for which of the given functions, can't conclude about location of  a relative…

Q: Consider the function f(x, y) = e^(10x - x^2 -10y - y^2). Find and classify all critical points of…

A: The given question can be solved as shown in step 2.

Q: Sketch the graph of a differentiable function y = ƒ(x) through the point (1, 1) if ƒ′(1) = 0 and a.…

A: We need to Sketch the graph of a differentiable function y = ƒ(x) through the point (1, 1) if ƒ′(1)…

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

A:

Q: function, that is 0 everywhere except at t=0, is know as:

A:

Q: x², if xs1 4. Let f(x) = . Find f. (1) andf'(1). Does f'(1) exists? 2x, if x>1 Show that the…

A: 4. fx=x2,if x≤12x,if x&gt;15. y=f(x)=x2-3x

Q: Suppose it is known that for a given differentiable function y = f(æ), its local linearization at…

A:

Q: 7. Find all values of x on the graph of f(x)=(x-1)´(2x+1) at which the tangent line is horizontal.…

A:

Q: 9. An equation of the line normal to the graph of f(x)=, at (1,–1) is (a) 2x - y -3 -0 (b) 2x + y…

A: Explanation: Given that  f(x)=xx-2 at (1,-1)   Concept Used: To find the normal firstly find the…

Q: Suppose f(x) is an invertible differentiable function and the graph of f passes through the points 1…

A: