(a) Find the slope of the curve y =x- 3x - 4 at the point P(3, - 4) by finding the limit of the secant slopes through point P. (b) Find an equation of the tangent line to the curve at P(3, - 4). ..... (a) The slope of the curve at P(3, – 4) is (Simplify your answer.)

(a) Find the slope of the curve y =x- 3x - 4 at the point P(3, - 4) by finding the limit of the secant slopes through point P. (b) Find an equation of the tangent line to the curve at P(3, - 4). ..... (a) The slope of the curve at P(3, – 4) is (Simplify your answer.)

Name: How would I find a, and b based on the given points? (a) Find the slop
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Description: How would I find a, and b based on the given points? (a) Find the slope of the curve y =x - 3x - 4 at the point P(3, - 4) by finding the limit of the secant slopes through point P.(b) Find an equation of the tangent line to the curve at P(3, – 4)....

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?
A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of the slope of the secant line through the point B. Find the equation of the tangent line to the curve at (2, -4)
find the slope of a curve y = x2-2x-2 at the point P(3,1) by finding the limit of the secant slopes through point P
The tangent line to the graph of y = h(x) at the point ( -1, 4) passes through the point (3, 6).Find h( -1) and h' ( -1).
find the slope of the curve y=x^2-4x-4 at the point P(3,-7) by finding the limiting value of the slope of the secant lines through point P. find an equation of the tangent line to the curve at P(3,-7).
Find an equation of the tangent line to the parabola y = x2 - 6x + 7 at the point (2, -1). SOLUTION From the previous example, we know the derivative of f(x) = x2 - 6x + 7 at the number a is f '(a) = 2a - 6. Therefore the slope of the tangent line at (2, -1) is f '(2) = 2(2) - 6 = . Thus an equation of the tangent line, shown in the figure, is y - ( ) = (x - )or y = x + 3
Find the slope of the tangent to the graph of f(x) = x^2 + 1 at the point (2, 5). Use the method of finding the slope of the secant between (2, 5) and a neighboring point, and moving the neighboring point closer and closer to (2, 5). What is important here is the method, not the answer, so show your work very clearly. A diagram is needed, but you do not need to draw all your secant lines if that becomes difficult.
The line tangent to the graph of y=x3 at the point where x=0.2 crosses the x-axis at the point where:
a. Find the slope of the tangent line to the graph of f at the given point.b. Find the slope-intercept equation of the tangent line to the graph of f at the given point.f(x) = 2x + 3 at (1, 5)
a) Use the limit definition of the derivative to find the slope of the line tangent to the curve y = √(2x+1) at a=4. b) Use your result of part (a) to find the equation of the line tangent to the curve at the point x= 4, y= 3. Give clear steps and explanations.
FIND THE DERIVATIVE OF THE FUNCTION BY THE LIMIT PROCESS. SHOW YOUR STEP BY STEP SOLUTIONS. 2. h(s)=3+2/3S 3. f(x)= 5-2/3X
Find an equation of the tangent line to the graph of the function f defined by the equation at the indicated point. y2 − x2 = 144; (6, 6√5)