for the following f defined by f(x)=4x^2+3x+2. find the following values.
a. f(-2)=
b. f(-x)=
c. -f(x)=
df(x+h)=
please show work
a. To find f(-2), we substitute -2 into the function f(x):
f(-2) = 4(-2)^2 + 3(-2) + 2
Now, simplify:
f(-2) = 4(4) - 6 + 2
= 16 - 6 + 2
= 12
Therefore, f(-2) = 12.
b. To find f(-x), we substitute -x into the function f(x):
f(-x) = 4(-x)^2 + 3(-x) + 2
Now, simplify:
f(-x) = 4x^2 - 3x + 2
c. To find -f(x), we multiply f(x) by -1:
-f(x) = -1 * (4x^2 + 3x + 2)
Now, distribute -1 to each term within the brackets:
-f(x) = -4x^2 - 3x - 2
d. To find the derivative, df(x), we differentiate the function f(x) with respect to x. For this, we'll use the power rule:
f(x) = 4x^2 + 3x + 2
Taking the derivative with respect to x, we get:
df(x) = d/dx (4x^2) + d/dx (3x) + d/dx (2)
Applying the power rule, the derivatives of each term are as follows:
df(x) = 8x + 3 + 0
Simplifying,
df(x) = 8x + 3
Therefore, the derivative of f(x) with respect to x is 8x + 3.