8 If f(x) = 14 +₁ 7 0 O f(x) 14+ f(r) x", then f"(x) is co

Q: x if x20 If Ax) = -x2 then f'(0) if x <0

A: Given function, fx=x2      if x≥0-x2   if x&lt;0

Q: -5x2 – 3 If f(x) = then f'(0) is 4х + 2 O - 3 О 13 O - 1/3 Оз

A: Solving the problem by obtaining the derivative.

Q: 2+x 5. Given f(x) =<tX Find X-4 %3D a) fe) b) f(a+1) c) f(x) + f(h)

A:

Q: For the function f(x)=√x+3 ifx<2 2x-3 ifx22 evaluate the following: ,

A: Function f(x) is two different value of different value of x

Q: 10. Given the functions f(x) = x² – 3 and g(x) = Vx, find the following. - a) (f o g)(x) b) (go…

A:

Q: 3x10 + 3a5 + 5æ² + 7. What particular solution that satisfies Suppose f'(x) 455 -? 66 f(1)

A:

Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: b) y =1+ f(z)=2x-2 O 1ks f-(z)=-1 O 2 34s (2)=2x-1

A: Step 1 Replace y with x and x with y  Step 2 Then solve for y in this equation  Step 3 Replace y…

Q: 17. Given f (x) = -4, find f-(x). b. d. C. a. d.

A: The given function is

Q: If f(x) 2 0, then [ flx)dx Select one: O True O False

A: F(x) is postitive so area under the curve is above x-aXis so it is positive.

Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: f (æ, t) = e-t function fea - fu = 0 provides equality. True False

A: Given the function fx, t=ex-t We need to check the validity of fxx-ftt=0 to get the correct option.

Q: Determine the value of k for which f'(3)-2, if f(x) = x+*. x-1

A: Given a function,f(x)=x+kx−1To find : the value of k for which f′(3)=2.Using the quotient…

Q: f(x) = 2x + 9. Find f inverse. * O (9-2x) / 2 -2x-9 O(x-9) /2

A:

Q: 7. (a) f(x) < 0 X= -1 X = 1 (b) f(x) 2 0 41 y. 3 y = 0 -3 3- -3

A: Graph of the function is given we have to finda) f(x)&lt;0b) f(x)≥0

Q: Provide the table of signs for both f' and ff'.

A: Given function is fx = x+334x-12 = x4 +12x-1+16x-12 +114. Also, given that f'x = x-9x+324x-13    and…

Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

A:

Q: Eliminate the arbitrary constant on the given equation: y = C1e-2x + Cze2x

A:

Q: 3. Suppose that f(1) = 2, f(4) 7, f'(1) 5, f'(4) = 3, and f" is continu- %3D | af" (x) da. ous. Find…

A: The given data is: f1=2f4=7f'1=5f'4=3  f'' is continuous  To find the value of ∫14xf''xdx.

Q: 2. f(x) f(0) S() 0 f(0) f x) 0I=

A: First we  find equation of line that is  y= mx+b Here m=-2 and b = 2 So equation form and it is y=…

Q: 8. Simplify f(x + h) - f(x), where: a) f(x) = 2x + 3 b) f(x) = 1 c) f(x) = x² %3D 1 2.

A: a) f(x)=2x+3b) f(x)=x2c) f(x)=11

Q: 22. Find f/(x) and simplify 1 -1 a) f(z) 3-52+1 3 b) f(x) 1.8Vc) f(x) = 32

A: Given, functions

Q: Given f (x) = x³ - 3x – 1,x 2 2, find (f~')'(-1)

A:

Q: 5x -1 7. f(x) = 3. a) HA at b) VA at

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: If f(x) =>(1- (sinx)²)" .Determine the value of f)

A: use the trigonometric identities to simplify and the solve. detailed explanation is in step 2 answer…

Q: 6. Given that f(x) = 3x? + 1, find +h)=[(x)

A: Given f(x)=3x2 + 1

Q: 4) If f(x) = [√9+ x²] then f(R) =_

A: