Question

The derivative of a function f(x) is given by f'(x)=3x^2-6x+4. The tangent line at the point (2,9) is parallel to another tangent line at the point ( a,b) . Find a .

Answer 1

Answer:2

Explanation:

Given

The derivative of a function is
`f'(x)=3x^2-6x+4`

The slope at (2,9) is

`\Rightarrow 3(2)^2-6* 2+4=4`

the tangent at (2,9) is parallel to another tangent at (a,b) i.e. their slopes are equal

`\Rightarrow 4=3a^2-6a+4\\\Rightarrow 3a^2-6a=0\\\Rightarrow\ 3a(a-2)=0\\\Rightarrow a=0\ \text{or}\ a=2`