On this problem, you may use a computer to calculate the derivative. Consider the function f(t)...

On this problem, you may use a computer to calculate the derivative. Consider the function f(t) = (2t^2) / (3t^2 + 1) :

(a) On what intervals is the function concave up, and on what invervals is it concave down? Why? (b) (5 points) On what intervals is the function increasing, and on what intervals is it decreasing? Why?

(b) On what intervals is the function increasing, and on what intervals is it decreasing? Why?

Expert Solution

milcah answered 2 years ago

For the following exercises, use the definition of derivative to calculate the derivative of each function. f(x) = 5π

For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 5π

For the following exercises, use the definition of derivative to calculate the derivative of each function. f(x) = 3x3 − x2 + 2x + 5

For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 3x3 − x2 + 2x + 5

Find the derivative of the function f(t)=arccsc⁡〖(-t^2)〗 f(x)=arccot⁡√x y=ln⁡〖t^2 〗-arctan⁡〖t/2〗 f(x)=arcsec⁡x+arccsc⁡x...

Find the derivative of the function f(t)=arccsc⁡〖(-t^2)〗 f(x)=arccot⁡√x y=ln⁡〖t^2 〗-arctan⁡〖t/2〗 f(x)=arcsec⁡x+arccsc⁡x y=arctan⁡〖x/2〗+1/(2(x^2+4)) Use implicit differentiation to find an equation of the tangent line the graph of the equation at the given point. arctan⁡(x+y)=y^2+π/4, (1,0)

1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the...

1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the derivative function f'(x)f′(x) to determine where the function f(x)=2x^3−27x^2+108x+13 is increasing. 3.Use the derivative function f'(x)f′(x) to determine where the function f(x)=2x^3−27x^2+108x−12 is decreasing. 4.Find each value of the function f(x)=−x^3+12x+9 where the line tangent to the graph is horizontal. x=

Part A. If a function f has a derivative at x not. then f is continuous...

Part A. If a function f has a derivative at x not. then f is continuous at x not. (How do you get the converse?) Part B. 1) There exist an arbitrary x for all y (x+y=0). Is false but why? 2) For all x there exists a unique y (y=x^2) Is true but why? 3) For all x there exist a unique y (y^2=x) Is true but why?

Find the derivative of the following function. Do not use limits. f(x)=x5+(x3/3)-5x2+2x-3. Then, calculate the value...

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1) The graph of the derivative f ' of a continuous function f is shown. (Assume...

1) The graph of the derivative f ' of a continuous function f is shown. (Assume the function f is defined only for 0 < x < ∞.) (a) On what interval(s) is f increasing? (2a) On what interval(s) is f decreasing? (b) At what value(s) of x does f have a local maximum? (2b) At what value(s) of x does f have a local minimum? x=? (c) On what interval(s) is f concave upward? (2c) On what interval(s) is...

A) Find the derivative of the function f by using the rules of differentiation. f(x) =...

A) Find the derivative of the function f by using the rules of differentiation. f(x) = 380 B)Find the derivative of the function f by using the rules of differentiation. f(x) = x0.8 C) Find the derivative of the function f by using the rules of differentiation. D)Find the derivative of the function. f(u) = 10 u E)Find the derivative of the function f by using the rules of differentiation. f(x) = 9x3 - 2x2 + 1 u u

State the condition on the derivative f' that can be used to show that a function f is increasing.

State the condition on the derivative f' that can be used to show that a function f is increasing. b Define the function arctan. c Explain how one, starting from the definition of arctan, may derive an expression for the derivative of this function, and carry out that calculation.

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x +...

Suppose that f is a differentiable function with derivative f" (x) = (x − 3)(x + 1)(x + 5). Determine the intervals of x for which the function of f is increasing and decreasing Explain why a positive value for f" (x) means the graph f(x) is increasing For f(x) = 2x2- − 3x2 − 12x + 21, find where f'(x) = 0, and the intervals on which the function increases and decreases Determine the values of a, b, and...

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