Homework Statement
Find the equation of the line tangent to y=(x²+3x)² (2x-2)³, when x=8 Homework Equations
The Attempt at a Solution
dy/dx = 56x^6+144x^5-240x^4-320x^3+504x^2-144x...or...8x(x+3)(x+2)(7x-3)(x-1)²
dy/dx (8) = 18282880
y(x) = 21249536
Equation of tangent line at x=8;
y=...
My teacher has a definition where
\lim_{x\to a}f(x) = f(c)
It was my understanding that f(x) = 3x^2, a = -5, and f(c) = 2x+c. So once I knew the answer to the limit, i knew that f(c) = 75, thus 2x+c must also be 75. Maybe I am misunderstanding the definition. Can anyone clarify?
Homework Statement
Find c such that it makes f(x) continuous.
Homework Equations
f(x)=\begin{cases}
2x+c&x < -5\\
3x^2&-5 \leq x < 0\\
cx^2&0 \leq x\\
\end{cases}
The Attempt at a Solution
I know that
\lim_{x\to 5^-}3x^2 = 2x+c
and
\lim_{x\to...