If the function is f(x)= 3x^4-5x^2+6, how to find what f'(2) equals to?

Question

Would it equal -76?

Answer 1

Let's see.

If f(x) = 3x⁴-5x²+6, then f'(x) = 12x³-10x

So, f'(2) = 12(2)³-10(2) = 12(8) -20 = 96-20 = 76.

Agreed!

Here is a Desmos graph for confirmation. Visit the graph to see some tangent lines to f(x) too.

desmos.com/calculator/tuau77zaqu

Answer 2

f(x) = 3x⁴ - 5x² + 6

f'(x) = 12x³ - 10x

So, f'(2) = 96 - 20 = 76

Answer 3

When we take the derivative, we multiply the coefficient by the variable's exponent, and then we subtract that variable's exponent by 1. So, f'(x) = 4*3x^4-1 - 2*5x^2-1 + 0*6 = 12x^3 - 10x

Since we want to know what f'(2) is equal to, we will plug in a 2 everywhere there is an x, so we will have:

12(2)^3 - 10(2) = 12(8) - 20 = 96 - 20 = 76

So the answer is actually 76. You were right about 76; it's just the answer needs to be positive, not negative.

Answer 4

No, f'(2) ≠ -76