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Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 4x – 3/x, (1, 1) Step 1 We can find the equation of a line by using the Point-Slope formula y - yo = m(x - xo). This means that we need to find the slope m of the line and a point (xor Yo on the line. We begin by finding the slope. The line tangent to y at (xo, Yo) will have the slope m = f'(x,). We have y = y = 4x – 3/x. Since 3x = 3x/2, then 3 y'=

Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 4x – 3/x, (1, 1) Step 1 We can find the equation of a line by using the Point-Slope formula y - yo = m(x - xo). This means that we need to find the slope m of the line and a point (xor Yo on the line. We begin by finding the slope. The line tangent to y at (xo, Yo) will have the slope m = f'(x,). We have y = y = 4x – 3/x. Since 3x = 3x/2, then 3 y'=

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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We have rewritten the given function as f(x) = x* + 5x³, and we wish to find the derivative f'(x). In other words, we need to find the following. f'(x) = (x* + 5x³) dx Recall the sum rule, which states that if g and h are both differentiable, then the following is true. dx Applying this rule allows us to rewrite as follows. -(xª + 5x³) dx f'(x) = -(5x³) dx dx
Transcribed Image Text:We have rewritten the given function as f(x) = x* + 5x³, and we wish to find the derivative f'(x). In other words, we need to find the following. f'(x) = (x* + 5x³) dx Recall the sum rule, which states that if g and h are both differentiable, then the following is true. dx Applying this rule allows us to rewrite as follows. -(xª + 5x³) dx f'(x) = -(5x³) dx dx
Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 4x – 3/x, (1, 1) Step 1 We can find the equation of a line by using the Point-Slope formula y – Yo = m(x - xn). This means that we need to find the slope m of the line and a point (Xo, Yo) on the line. We begin by finding the slope. The line tangent to y at (xo, Yo) will have the slope m = f'(x,). We have y = y = 4x – 3/x. Since 3/x = 3x/2, then y' =
Transcribed Image Text:Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 4x – 3/x, (1, 1) Step 1 We can find the equation of a line by using the Point-Slope formula y – Yo = m(x - xn). This means that we need to find the slope m of the line and a point (Xo, Yo) on the line. We begin by finding the slope. The line tangent to y at (xo, Yo) will have the slope m = f'(x,). We have y = y = 4x – 3/x. Since 3/x = 3x/2, then y' =
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