Let f(x)=x^2+5x-3.
Find f′(x) and find f′(1).
f'= 2x+5
F'(1) is 7
thanks allie but i need someone to show the work to how they got those answers too please :)
She found the derivative of the equation, and then simply plugged in a one for the (x) after it was in its derivative form.
yes I know that but I need to steps for how you find the derivative.
basically just the power rule:
y = x^n
y' = n*x^(n-1)
To find the derivative f'(x) of a function f(x), you can use the power rule. The power rule states that if you have a term of the form x^n, then the derivative will be n times x^(n-1).
Given that f(x) = x^2 + 5x - 3, let's find f'(x):
f'(x) = (d/dx) [x^2 + 5x - 3]
The derivative of each term separately:
(d/dx) [x^2] = 2x^1 = 2x
(d/dx) [5x] = 5
(d/dx) [-3] = 0
So, putting it all together:
f'(x) = 2x + 5
To find f'(1), we substitute x = 1 into the expression we obtained for f'(x):
f'(1) = 2(1) + 5 = 2 + 5 = 7
Therefore, f'(1) = 7.