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If f(x) = x−6x^2 find (f(x + h) − f(x))/h

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varshamittal029

The value of  (f(x + h) − f(x))/h is 1 - 6h - 12x.

For any function, say f(x) = x + a, the value of f(x+b) = (x + b) + a or (x + b + a)

Here, we are given that

f(x) = x−6x^2

and we need to find the value of (f(x + h) − f(x))/h

Firstly,

f(x + h) = (x+h) - 6(x+h)^2

Now, f(x + h) − f(x) = (x+h) - 6(x+h)^2 - (x−6x^2)

= (x+h) - 6(x+h)^2 - x + 6x^2

= x - x + h - 6(x^2 + h^2 + 2xh) + 6x^2

= h - 6x^2 - 6h^2 - 12xh + 6x^2

=  h - 6x^2  + 6x^2 - 6h^2 - 12xh

= h - 6h^2 - 12xh

= h( 1- 6h - 12x)

Thus, (f(x + h) − f(x))/h = [h( 1- 6h - 12x)] / h

= 1 - 6h - 12x

Therefore, the value of  (f(x + h) − f(x))/h is 1 - 6h - 12x.

Learn more about functions here-

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