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Section 2.1 Homework

1. Consider the parabola

y = 5 x - x^{2}

(a) Find the slope of the tangent line to the parabola at the point (1, 4).
(b) Find an equation of the tangent line in part (a).
y =
(c) Graph the parabola and the tangent line.

2. Consider the curve

y = x - x^{3}

(a) Find the slope of the tangent line to the curve at the point (1, 0).
(b) Find an equation of the tangent line in part (a).
y =

3. Find an equation of the tangent line to the curve at the given point.

$y = x^{3} - 3 x + 2, (3, 20)$

4. Find an equation of the tangent line to the curve at the given point.

$y = \sqrt{x}, (25, 5)$

5. If f(x) =

9 x^{2} - x^{3}, f i n d f ‘ (1) a n d u s e i t t o f i n d a n e q u a t i o n o f t h e \tan g e n t l i n e t o t h e c u r v e y = 9 x^{2} - x^{3} a t t h e p o i n t (1, 8)

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Section 2.1 Homework Answers

1. Consider the parabola

y = 5 x - x^{2}

(a) Find the slope of the tangent line to the parabola at the point (1, 4).
(b) Find an equation of the tangent line in part (a).
y =
(c) Graph the parabola and the tangent line.

Answers:

a. 3

b. y=3x+1

This question is taken from Math 261 – Calculus I » Spring 2022 » Homeworks

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