Q. 235.0( 2 Votes )

# Find the rate at which the function f(x) = x^{4} – 2x^{3} + 3x^{2} + x + 5 changes with respect to x.

Answer :

Given,

y = x^{4} – 2x^{3} + 3x^{2} + x + 5

We need to rate of change of f(x) w.r.t x.

Rate of change of a function w.r.t a given variable is obtained by differentiating the function w.r.t that variable only.

So in this case we will be finding dy/dx

As, y = x^{4} – 2x^{3} + 3x^{2} + x + 5

Now, differentiating both sides w.r.t x –

∴ )

Using algebra of derivatives –

⇒

Use:

∴

⇒

∴ Rate of change of y w.r.t x is given by –

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