Let f(2) V4.1 +3. f(0) - f(a) Using the definition of derivative at a point, f'(a)...
Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x2 + x - 1 the definition of the derivative f'(x) = lim f(x+h)-f(x) h h-0 What is the slope of tangent line to this curve at x = -1?
5. (10 points) Let f(x) = -(9x² +6x+2). Then according to the definition of derivative f'(x) = lim h0 (Your answer above and the next few answers below will involve the variables x and h. We are using h instead of Ar because it is easier to type) We can cancel the common factor — from the numerator and denominator leaving the polynomial Taking the limit of this expression gives us f'(x) = 6. (10 points) Let f(x) = x3...
Thank you. - Part 1: Limit of a difference quotient Suppose f(x) = – 5. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). X - 2 (f(5 + h) – f(5) lim h0 Him ( 15 + ) - 109 ) = lim ( = lim h0 | Part 2: Interpreting the limit of a difference quotient - Part 1: The derivative at...
(a) Let f(x) = 3x – 2. Show that f'(x) = 3 using the definition of the derivative as a limit (Definition 21.1.2). 1 (b) Let g(x) = ? . Show that y that -1 g'(x) = (x - 2)2 using the definition of the derivative as a limit (Definition 21.1.2).
Let f(x) = (4x + 1)2 . Using the limit definition of a derivative f'(a) = limh→0 f(a + h) − f(a) /h find f'(0)
2. Given f(x) = find the derivative using the definition of derivative. 3. Find A and B given that the function, f(x), is continuous at x = 6. V | f(x) = {B (Ar - 42 > 6 4. Find the slope of the tangent line to the curve 2.2 - 2xy + 3y2 = 10 at the point (1,2).
#23. Use the limit definition of the derivative to show why f(x) = (x - 5) is NOT differentiable at x = 5. (Hint: Compare the left- and right-hand limits of lim nits of lim f(5+h)-f(5) 102.) Is f(x) = (x - 5)% continuous at x = 5? What does the tangent line at the point (5,0) look like? 0
(1 point) Let f(x) = 3x - 2x + 9. Then according to the definition of derivative f'(x) = lim (Your answer above and the next few answers below will involve the variables x and h. We are using h instead of Ax because it is easier to type) We can cancel the common factor from the numerator and denominator leaving the polynomial Taking the limit of this expression gives us f'(x) = -4x+3
Let f(x) = Find f'(a) By using the limit definition of the derivative, algebra and limit laws T 20
2. Given f(x)=e*: (a) Find f'(x) using the definition of derivative, f'(x)= lim{{(x+h)-f(x)), by making h smaller and smaller. Round answer to two decimal places. (b) Evaluate f (1). (c) Carefully, graph f(x)=e-*, -15x52 using points every 0.5 units. (d) Find the equation of the tangent line at x = 1. Attach the graph of this line to the graph in (c).