Find the rate at which the function f (x) = x⁴ − 2x³ + 3x² + x + 5 changes with respect to x.

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Solution

$Rate = f' (x) = \frac{d}{d x} (x^{4} - 2 x^{3} + 3 x^{2} + x + 5) = \frac{d}{d x} (x^{4}) - 2 \frac{d}{d x} (x^{3}) + 3 \frac{d}{d x} (x^{2}) + \frac{d}{d x} (x) + \frac{d}{d x} (5) = 4 x^{3} - 2 (3 x^{2}) + 3 (2 x) + 1 + 0 = 4 x^{3} - 6 x^{2} + 6 x + 1$

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Similar questions

Q. Find the rate at which the function

f (x) = x^{4} - 2 x^{3} + 3 x^{2} + x + 5

changes with respect to x.

Q. The polynomial

f (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b

when divided by

(x - 1)

and

(x + 1)

leaves the remainders

5

and

9

respectively. Find the values of

a

and

b

When f(x) = $x^{4}$ -2 $x^{3}$ +3 $x^{2}$ -ax+b is divided by x+1 and x-1, we get remainders 19 and 5 respectively. Find the remainder when f(x) is divided by x-3.

Q. The polynomial f(x) = x⁴ − 2x³ + 3x² − ax = b when divided by (x − 1) and (x + 1) leaves the remainder 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when f(x) is divided by (x − 2).

Q. Find the interval in which the following function is increasing or decreasing.

f (x) = 5 + 36 x + 3 x^{2} - 2 x^{3}

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Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.

Rate = f'(x) =ddxx4-2x3+3x2+x+5 =ddxx4-2ddxx3+3ddxx2+ddxx+ddx5 =4x3-23x2+32x+1+0 =4x3-6x2+6x+1

Find the rate at which the function f (x) = x⁴ − 2x³ + 3x² + x + 5 changes with respect to x.

$Rate = f' (x) = \frac{d}{d x} (x^{4} - 2 x^{3} + 3 x^{2} + x + 5) = \frac{d}{d x} (x^{4}) - 2 \frac{d}{d x} (x^{3}) + 3 \frac{d}{d x} (x^{2}) + \frac{d}{d x} (x) + \frac{d}{d x} (5) = 4 x^{3} - 2 (3 x^{2}) + 3 (2 x) + 1 + 0 = 4 x^{3} - 6 x^{2} + 6 x + 1$