What is the slope of f(x)=−x3−3 at x=-1?

Question

Konnor Davidson · Accepted Answer

First of all, let&#039;s compute the derivative of f(x), indicated as f&#039;(x):f(x)=−x3−3⇒f′(x)=−3x2In fact, to derive a sum you must derive each single term. The first term is a power of x, and the derivative of xn is nxn−1. So, the derivative of x3 is 3x3−1=3x2, andsince we had a minus sign in front of it, we will have to change signs: the derivativeof −x3 is 3x3−1=−3x2.As for the second term, the derivative of a number is always zero, which is why the term -3 has disappeared in the derivative.Now, just like our function f(x) associated a y with every x, in the same way our derivative f&#039;(x) associates, for every point x, the slope of the line tangent to the graph in the point (x, f(x))In other words, f&#039;(-1) is exactly the answer you are looking for. The computation isf′(−1)=−3(−1)2=−3⋅1=−3

klepbroek31s · Accepted Answer

Explanation:the slope is the value of f&#039;(-1)⇒f′(x)=−3x2⇒f′(−1)=−3(−1)2=−3Answer:slope =-3

What is the slope of \(\displaystyle{f{{\left({x}\right)}}}=-{x}^{{{3}}}-{3}\) at

Answered question

Answer & Explanation

New Questions in Calculus 1