Question

o f(x)=12x3+27x2−162x+12 o a. Find the slope of this function at x=2.​

Answer 1

Given:

f(x)=12x3+27x2−162x+12

x=2

To find:

The slope of this function at x=2

Solution:

First we need to substitute the values of x=2 in the function

f(x)=12x3+27x2−162x+12

Now we substitue it

f(2)= 12(2^3)+ 27(2^2)-162(2)+12

Now we calculate it

f(2)=  96+ 108-324+12

f(2)= -108

the final coordinates are

(2,-108)

But to find the gradient we need two points hence we will use x=0 to find the other two points

f(x)=12x3+27x2−162x+12

We substitute 0 here

f(x)=12(0^3)+27(0^2)−162(0)+12

f(0)= 12

Now we have both the co-ordinates

(0,12) (2,-108)

Now we can find the gradients using the formula

y2-y1/x2-x1 =m

(m is used to symoblise gradient)

m= -108-12 /2-0

m= -120/2

m= -60

Solution:

the slope of this function at x=2 is m=-60