(a) Find the slope of the curve yx2-5x-2 at the point P(3, 8) by finding the limiting value of the slope of the secant lines through point P (b) Find an equation of the tangent line to the curve at P(3, 8). (a) The slope of the curve at P(3, 8) is 1. (Simplify your answer.) (b) The equation of the tangent line to the curve at P(3, 8) is y |

(a) Find the slope of the curve yx2-5x-2 at the point P(3, 8) by finding the limiting value of the slope of the secant lines through point P (b) Find an equation of the tangent line to the curve at P(3, 8). (a) The slope of the curve at P(3, 8) is 1. (Simplify your answer.) (b) The equation of the tangent line to the curve at P(3, 8) is y |

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

See similar textbooks

Similar questions

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?
Find the slope of the curve y=x^3-3 at the point P(-2,-11) by finding the limiting value of the slope of the secants through P
Find the slope of the curve y=x2−3x−4 at the point P(2,−6) by finding the limiting value of the slope of the secant lines 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 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
The curve enters the window in the second quadrant, goes down and right, and exits the window nearly vertical at the approximate point (−7.2, −3). The curve reenters the window nearly vertical at the approximate point (−6.7, −3), goes up and right becoming less steep, crosses the x-axis at x = −5, goes up and right becoming more steep, and exits the window at the point (−3.3, 3). The curve reenters the window nearly vertical at the approximate point (−2.9, 3), goes down and right, changes direction at the approximate point (−1.5, 0.5), goes up and right, and exits the window nearly vertical at the approximate point (−0.1, 3). The curve reenters the window nearly vertical at the approximate point (0.2, 3), goes down and right, changes direction at the approximate point (1.6, −2), goes up and right, changes direction at the approximate point (4.3, 2.7), goes down and right, and exits the window nearly vertical at the approximate point (5.8, −3). The curve reenters the window nearly…
a)Find an equation of the line tangent to the graph of y = x2 + 1 at the point (2, 5)b) Find an equation of the line perpendicular to the graph of y = x2 + 1 at (2, 5)c) Where is the line tangent to the graph of y = x2 + 1 horizontal
The tangent line to the graph of y = g(x) at the point (4, 5) passes through the point (7, 0). Find g(4) and g′(4).
Find the point (x0,y0) on the graph y=x^3 + 6x^2 +3x -5 at which the slope of the tangent line has its minimum value (enter your answer as a coordinate point in the form (* , *) (x0,y0) = _____________________
Find the slope of the curve y=x^3-14x at the given point P(1,-13) by finding the limiting value of the slope of the servants through P. Find the equation of the tangent line to the curve at P(1,-13)
Find an equation of the tangent line to the graph of Y = e2x-3 at the point (3/2,1).
[3] If the curve is defined by y= x⁴ - 8x³ + 22x²-24x+9, then what are the value/s of x for which the slope of the tangent line to the curve is zero?