Question 2: What is the slope of the tangent of the function13b(x) = a³ –a² + 2 x2at r = 2? This time, please draw your own figure (and estimate the slope by using what you havedrawn), and then also calculate the answer by setting up and calculating the appropriate limit.[ Hint: b(x + h) 3D 23-을22+2x + (z2 - 3x + 2)h + (z - 흙)h2 + 흉h3 ] 8.7-4-32-12-14-21-3-6.

The equation of the given function is bx=13x3-32x2+2x. Take the given function as y=13x3-32x2+2x.…

Answered: Question 2: What is the slope of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The equation of the given function is $b (x) = \frac{1}{3} x^{3} - \frac{3}{2} x^{2} + 2 x$ .

Take the given function as $y = \frac{1}{3} x^{3} - \frac{3}{2} x^{2} + 2 x$ .

When $x = 2$ , the value $y = \frac{1}{3} (2^{3}) - \frac{3}{2} (2^{2}) + 2 (2) = \frac{8}{3} - 6 + 4 = \frac{2}{3}$ .

This gives the point $(2, \frac{2}{3})$ on the graph of the function b.

Using a graphing utility, sketch the curve $y = \frac{1}{3} x^{3} - \frac{3}{2} x^{2} + 2 x$ and draw the tangent line at the point $x = 2$ on the function curve as shown below.

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