Differentiation p2

the straight line that "just touches" the curve at that point.

Tangents and normals

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What have you prepare before studying today?

Objectives

We will learn how to:
~ apply differentiation to gradients, tangents, and normals.
~ find second derivative.

​Yahya bin Abi Katsir رحمه الله

The line perpendicular to the tangent at the point A is called the normal at A.

Tangents and Normals

Math Response

Given the curve $$y=2x^2+\frac{8}{x^2}-9$$ ,

Find the coordinate lies on the curve for $$x=2$$

Type answer here

Correct Answer: 1

Deg^°

Rad

Math Response

Given the curve $$y=2x^2+\frac{8}{x^2}-9$$ ,

Find the first differentiation respect to x of the curve.

Type answer here

Correct Answer: 4x-16x^{-3}

Deg^°

Rad

Math Response

Given the curve $$y=2x^2+\frac{8}{x^2}-9$$ ,

Find the tangent line of the curve that passes through $$(2,1)$$ .

Type answer here

Correct Answer: y=6x-11

Deg^°

Rad

Math Response

Given the curve $$y=2x^2+\frac{8}{x^2}-9$$ ,

Find the normal line of the curve that passes through $$(2,1)$$ .

Type answer here

Correct Answer: x+6y=8

Deg^°

Rad

Math Response

A curve has equation $$y=\left(4-\sqrt[]{x}\right)^3$$ ,

Find the first of differentiation of y.

Type answer here

Correct Answer: -\frac{3\left(4-\sqrt{x}\right)^2}{2\sqrt{x}}

Deg^°

Rad

Math Response

A curve has equation $$y=\left(4-\sqrt[]{x}\right)^3$$ ,

Find the the normal at the point (4, 8)

Type answer here

Correct Answer: 3y=x+20

Deg^°

Rad

Math Response

A curve has equation $$y=\left(4-\sqrt[]{x}\right)^3$$ ,

Find the the normal at the point (9, 1)

Type answer here

Correct Answer: y=2x-17

Deg^°

Rad

Second Derivative

Math Response

Find $$\frac{d^2x}{dx^2}$$ of the following functions.

$$y=x^2+8x+4$$

Type answer here

Correct Answer: 2

Deg^°

Rad

Math Response

Find $$\frac{d^2x}{dx^2}$$ of the following functions.

$$y=5x^3-7x^2-5$$

Type answer here

Correct Answer: 30x-14

Deg^°

Rad

Math Response

Find $$\frac{d^2x}{dx^2}$$ of the following functions.

$$y=2-\frac{6}{x^2}$$

Type answer here

Correct Answer: -36x^{-4}

Deg^°

Rad