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Differentiation: Tangents and Normals

Total questions: 14

Worksheet time: 25mins

Name
Class
Date
1.

The equation of the straight line that goes through the point (3, 4) with a gradient of 2 is given as y=ax+by=ax+b  . Find the value of a.

(a)  

2.

The equation of the straight line that goes through the point (3, 4) with a gradient of 2 is given as y=ax+by=ax+b  . Find the value of b.

(a)  

3.

Given the function , f(x)=x3+2x2x+7f\left(x\right)=x^3+2x^2-x+7what is the gradient when x = -2 ?

(a)  

4.

Consider the function f(x)=x3+2x2x+7f\left(x\right)=x^3+2x^2-x+7 . The tangent to this curve at x=2x=-2 is given by y=ax+by=ax+b . Find the value of a.

(a)  

5.

Consider the function f(x)=x3+2x2x+7f\left(x\right)=x^3+2x^2-x+7 . The tangent to this curve at x=2x=-2 is given by y=ax+by=ax+b . Find the value of b.

(a)  

6.

Consider the function y=25x2+1x2y=\frac{2}{5}x^2+\frac{1}{x^2}  . The tangent to this curve at x=2x=2   is given by y=ax+by=ax+b  . Find the value of a.

(a)  

7.

Consider the function y=25x2+1x2y=\frac{2}{5}x^2+\frac{1}{x^2}  . The tangent to this curve at x=2x=2   is given by y=ax+by=ax+b  . Find the value of b.

(a)  

8.

Consider the function f(x)=x3+3x22x+4f\left(x\right)=x^3+3x^2-2x+4  , the normal to this curve at x=2x=-2  is given by y=ax+by=ax+b  . Find the value of a.

(a)  

9.

Consider the function f(x)=x3+3x22x+4f\left(x\right)=x^3+3x^2-2x+4  , the normal to this curve at x=2x=-2  is given by y=ax+by=ax+b  . Find the value of b.

(a)  

10.

What is the gradient of the function at x=3x=-3  ?

(a)  

11.

At x=1x=-1  the function is...

a)

Increasing

b)

Decreasing

12.

At x=4x=4  the function is...

a)

Increasing

b)

Decreasing

13.

Consider the function f(x)=1+4xf\left(x\right)=1+\frac{4}{x}  , the normal to this curve at x=2x=-2  is given by y=ax+by=ax+b  . Find the value of b.

(a)  

14.

Consider the function f(x)=1+4xf\left(x\right)=1+\frac{4}{x}  , the normal to this curve at x=2x=-2  is given by y=ax+by=ax+b  . Find the value of a.

(a)