Q. 605.0( 1 Vote )

# Fill in the

Given the first curve is y = 4x2 + 2x – 8

Now applying first derivative, we get

Now applying the sum rule of differentiation and the differentiation of the constant term is 0 we get

Now applying the power rule of differentiation we get

This is the slope of the first curve; let this be equal to m1.

m1=8x+2……(i)

Given the second curve is y = x3 – x + 13

Now applying first derivative, we get

Now applying the sum rule of differentiation and the differentiation of the constant term is 0 we get

Now applying the power rule of differentiation we get

This is the slope of the second curve; let this be equal to m2.

m2=3x2-1……(ii)

Now when the curve touch each other, there slope must be equal, i.e.,

m1=m2

8x+2=3x2-1

3x2-8x-1-2=0

3x2-8x-3=0

Splitting the middle term, we get

3x2+x-9x -3=0

x(3x+1)-3(3x+1)=0

(3x+1)(x-3)=0

(3x+1)=0 or (x-3)=0

Substituting in both the curves equation we get

For first curve, y = 4x2 + 2x – 8

For second curve, y = x3 – x + 13

Thus at both the curves do not touch

Substituting x=3 in both the curves equation we get

For first curve, y = 4x2 + 2x – 8

y=4(3)2+2(3)-8

y=4(9)+6-8=34

For second curve, y = x3 – x + 13

y= (3)3 – (3) + 13

y=27-3+13=37

Thus at x=3 both the curves do not touch

So the curves y = 4x2 + 2x – 8 and y = x3 – x + 13 do not touch each other.

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