Consider the function f(x) = Vx+1. (a) ( Compute f'(x) and f"(x). • (b) the point a = 0. O Write down the Taylor polynomials Tị and T2 of the function f at (c) Which value of b makes f(b) equal to V1.4?

Suppose f(x) = (x² + 1) · g(x), where g(x) f' (1) = 4. = mx + b. Find the slope, m, of g if f(0) 3 and 4 O -1/2 O 3 2

The number of bacteria in a refrigerated food product is given by N(T) = 24T2 - 109T+82, 4 < T < 34 where I' is the temperature of the T food. When the food is removed from the refrigerator, the temperature is given by T(t) = 4t + 1.5, where t is the time in hours. Find the composite function N(T(t)): N(T(t)) Find the time when the bacteria count reaches 11040. Give your answer accurate to at least 2 decimal places. Time Needed = hours

Differentiate the function. h'(t) h(t) = √t-7et - 0/1 ) - 70 ² Tet 7- (1) ( X

Find f '(a). 8t + 18 f(t) t + 3

Find f such that f'(x) = f(x) = 5 LO √√x X f(16) = 50. h

Find f"(x) if fƒ (x) = √√√5 - 4x. Show work: = -2(-1)(-4 5 points) The second derivative has been (x + 3)²(x − 2). Use interval test. oncave upward or concave downward.

Let f(x)=√x² + 5. After simplifying f'(x) is f'(2) is f"(x) is and f"(2) is Round to 4 decimal places when needed. Round to 4 decimal places when needed.

Find f(t). f(t) : = 21152 1 5 + 4s ـ ls2 }

compute ref(i) when f(z)=sqrt(z-1) and f(0)=-i