1. Find f '(−4), if f(x) = (5x2 + 6x)(3x2 + 7). Round your answer to the nearest integer. Use the hyphen symbol, -, for negative
values. 2. Find f'(x) for f(x) = −7x2 + 4x − 10.
14x − 10
−14x + 4
14x + 4
None of these
3.If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) = 2, then find h '(1) if h(x) = f(x) g(x).
−9
−24
0
24
4.Find the coefficient of the squared term in the simplified form for the second derivative, f "(x) for f(x) = (x3 + 2x + 3)(3x3 − 6x2 − 8x + 1). Use the hyphen symbol, -, for negative values.
3.If f and g are differentiable functions for all real values of x such
that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) =
2, then find h '(1) if h(x) = f(x) g(x).
h (x) = f(x) g(x) => h '(x) =. chain rule => f '(x) g(x) + f(x) g '(x)
4.Find the coefficient of the squared term in the simplified form for
the second derivative, f "(x) for f(x) = (x^3 + 2x + 3)(3x^3 − 6x^2 − 8x +
1). Use the hyphen symbol, -, for negative values.
You can tell that without all the calculus if you realize that the squared term comes from the term with the power 4 (because when you find the second derivative the power decreases two units). And that term is - 8x^4
And the second derivative of -8x^4 is -8*4*3 x^2 = -96x^2, where you see the coefficient is -96.
