For the following exercises, use the definition for the derivative at a pointto find the derivative of the functions. f(x) = −x2 + 4x + 7

For the following exercises, use the definition for the derivative at a pointto find the derivative of the functions.

f(x) = −x2 + 4x + 7

Solutions

Expert Solution

The derivative of function f at x = a is given by the formula:

f\'(a) = limx→a[{f(x) – f(a)}/(x – a)]

Consider the Following function:

f(x) = -x2 + 4x + 7

Determine the derivative of function f(x) = -x2 + 4x + 7 as follows:

f\'(a) = limx→a[f(x) – f(a)/(x – 1)]

= limx→a[(-x2 + 4x + 7) – (-a2 + 4a + 7)/(x – a)]

= limx→a[-(x2 – a2) + 4(x – 1)/(x – a)]

= limx→a[-(x – a)(x + a) + 4(x – a)/(x – a)]

Further simplify:

f\'(a) = limx→a[-(x + a) + 4]

= -(a + a) + 4

= -2a + 4

Junaid answered 1 year ago

Next > < Previous

Related Solutions

For the following exercises, use the definition for the derivative at a pointto find the derivative of the functions. f(x) = −x2 + 4x + 7

For the following exercises, use the definition for the derivative at a pointto find the derivative of the functions.f(x) = −x2 + 4x + 7

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

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

1. Use the definition of convexity to prove that the function f(x) = x2 - 4x...

1. Use the definition of convexity to prove that the function f(x) = x2 - 4x + 8 is convex. Is this function strictly convex? 2. Use the definition of convexity to prove that the function f(x)= ax + b is both convex and concave for any a•b ≠ 0.

What is the Derivative of f(x)=(4x^7)^5

Find the Derivative of the f(x)

Two questions: 2) Use the limit definition of the derivative to find the derivative of f(x)=...

Two questions: 2) Use the limit definition of the derivative to find the derivative of f(x)= x^3 - 9x 3) Using limits, find an equation of the line tangent to the function of g(x)= 4/x^2 at x= -2 Show All Work please! thank you :)

2. Find the following derivative y=4x?

2. Find the following derivative y=4x? 3. Find any maximum or minimum values of the function y(x)=1+x/e4x. Use a sign chart or a second derivative test to verify the answer(s) you get is a max or min.

For f(x)=9x+5 and g(x)=x2 find the following composite functions and state the domain of each a)...

For f(x)=9x+5 and g(x)=x2 find the following composite functions and state the domain of each a) f o g b) g o f c) f o f d) g o g a. the domain of f o g is b. (g o f )(x)= a. the domain of g o f is c. ( f o f )(x)= the domain of f o f is d. ( g o g)(x)= the domain of g o g is

a) Find the value of the Wronskian of the functions f = x^7 and g = x^8...

a) Find the value of the Wronskian of the functions f = x^7 and g = x^8 at the piont x = 1. b) Let y be the solution of the equation y ″ − 5 y ′ + 6 y = 0 satisfying the conditions y ( 0 ) = 1 and y ′ ( 0 ) = 2. Find ln ⁡ ( y ( 1 ) ). c) Let y be the solution of the equation y ″ + 2 y ′...

prove using the definition of derivative that if f(x) and g(x) is differentiable than (f'(x)g(x) -...

prove using the definition of derivative that if f(x) and g(x) is differentiable than (f'(x)g(x) - f(x)g'(x))/g^2(x)

Subjects