Question

(a) Find the slope of the tangent line to the parabola $y=x^{2}+3 x$ at the point $(-1,-2)$ (i) using Definition 1 (ii) using Equation 2 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point $(-1,-2)$ until the parabola and the tangent line are indistinguishable.

          (a) Find the slope of the tangent line to the parabola $y=x^{2}+3 x$ at the point $(-1,-2)$
(i) using Definition 1
(ii) using Equation 2
(b) Find an equation of the tangent line in part (a).
(c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point $(-1,-2)$ until the parabola and the tangent line are indistinguishable.

Added by Tyler W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

03/14/2023

Step 1

Plugging in the values, we get: \begin{align*} m&=\lim_{h\to 0}\frac{(-1+h)^2+3(-1+h)-(-2)}{h}\\ &=\lim_{h\to 0}\frac{h^2+h}{h}\\ &=\lim_{h\to 0}(h+1)\\ &=1 \end{align*} Show more…

Show all steps

Thanks for your feedback!

(a) Find the slope of the tangent line to the parabola $y=x^{2}+3 x$ at the point $(-1,-2)$ (i) using Definition 1 (ii) using Equation 2 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point $(-1,-2)$ until the parabola and the tangent line are indistinguishable.