Question

1) Find f'(x) by evaluating lim h->0 (f(x+h) - f(x)) / h When f(x) is given as follows: f(x) = sqrt(2x+5) 2) Given the function f(x) = 3x^2 - 5x + 1 (a) find the slope of the secant line through the points (2,3) and (3,13). (b) find the equation of the tangent line to the parabola y = f(x) at the point (2,3). slope of tangent line is f'(2) = lim h->0 (f(2+h) - f(2)) / h

          1) Find f'(x) by evaluating
lim h->0 (f(x+h) - f(x)) / h
When f(x) is given as follows:
f(x) = sqrt(2x+5)

2) Given the function f(x) = 3x^2 - 5x + 1
(a) find the slope of the secant line
through the points (2,3) and
(3,13).

(b) find the equation of the tangent
line to the parabola y = f(x) at
the point (2,3).
slope of tangent line is
f'(2) = lim h->0 (f(2+h) - f(2)) / h

1) Find f'(x) by evaluating
lim h->0 (f(x+h) - f(x)) / h
When f(x) is given as follows:
f(x) = sqrt(2x+5)

2) Given the function f(x) = 3x^2 - 5x + 1
(a) find the slope of the secant line
through the points (2,3) and
(3,13).

(b) find the equation of the tangent
line to the parabola y = f(x) at
the point (2,3).
slope of tangent line is
f'(2) = lim h->0 (f(2+h) - f(2)) / h

Added by Nicholas G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

12/11/2023

Step 1

Find the derivative of f(x) using the limit definition of the derivative: f'(x) = lim h->0 (f(x+h) - f(x))/h f'(x) = lim h->0 ((3(x+h)^2 - 5(x+h) + a) - (3x^2 - 5x + a))/h f'(x) = lim h->0 (6xh + 3h^2)/h f'(x) = 6x Show more…

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Find f'(x) by evaluating lim h->0 (f(x+h) - f(x))/h when f(x) is given as follows: f(x) = sqrt(2x+5). Given the function f(x) = 3x^2 - 5x + 1. (a) find the slope of the secant line through the points (2,3) and (3,13). (b) find the equation of the tangent line to the parabola y = f(x) at the point (2,3). slope of tangent line is f'(2) = lim h->0 (f(2+h) - f(2))/h