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- Determine the linear approximation for 2√x at x = 5. Use the linear approximation to approximate the value of 2√5.12Find a point c satisfying the MVT for the given function and interval. ?=x2/3, [0,8]Consider the function y = 3(square root of x) + 8. What is the value of C in the interval [4, 9] such that f(c) = fave ?
- Consider the function h(t)=t4f(t) with f a differentiable function.Write down the function h'(t)I understand part A where g is not continuous, but I dont understand the differentiable part. Why is it (x=2)? And the solution, why is it (-2(x-1)) and (-2(x-3))? Thank you again for all your help.Finad the linearization at the given points. f(x)= 6/x^2 at (2, 3/2)
- a. On what interval(s) is f(x) increasing? Justify. b. What is the concavity of f(x) at x=2? Explain your reasoning. c. Find the tangent line to f(x) at x=0.Find the absolute extrema of the function on the closed interval. y = 3 − ∣t − 3∣, [−1, 5]Answer 5 and 6 wshow solution Determine whether each of the following functions is (a) continuous (b) differentiable
- Does knowing that a function g(t) isdierentiable at t = 7 tell you anything about the dierentiabilityof the function 3g at t = 7? Give reasons for your answer.Assume that h(x) = f(g(x)) , where both f and g are differentiable functions. If g(-1)=2, g'(-1)=3, and f'(2)=-4 , what is the value of h'(-1) ?Let h(x)=f(g(x)), where f and g are differentiable on their domains. If g(−1)=2 and g′(−1)=7, what else do you need to know to calculate h′(−1)?