4. Find the value of the constant b for which f is continuous at a = - -1 and determine f(-1). 5 x < -1 bx³7 x ≥ −1 f(x) = giả = ={₁

Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

A: Given,

Q: (g) Suppose the first derivative of f(x) is f'(z) = z - 62 + 11z – 6. Where is f(z) increasing? Use…

A:

Q: 4. Let f be the function given by f(x) = 4-x. g is a function with derivative given by g'(x) =…

A: Given f( x ) = 4 - x

Q: Consider the function f(x) = 3x² + 30x + 83 Determine an expression for the derivative of f(x).

A: f(x)=3x2+30x+83

Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

A: A function f(x) is continous at x = a when:

Q: 5. Find all the zeroes of the function f(x) = - 0.5x? + 2.5 x +4.5 using False Position Method…

A:

Q: At which x location on the graph of f(x) = -x² - 2x + 15 is the slope of the tangent 0?

A:

Q: 6. Use the definition of the derivative to show that the function f(z) = Z is nowhere…

A:

Q: 2. What is the second derivative of f(x) = - ²x³²x²+6? f"(x) = 5x² - ²³√x f"(x) = 10x + √√√x+6 a. b.…

A:

Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.