The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.
Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.
By the fundamental theorem of calculus,
The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so
Sure, each of the following lines.
8x-6+3x-1
11x-6-1
and, 11x-7
The answer is
4 I hope this helps
Answer:
x = -1, y = -4
Step-by-step explanation:
Let's solve our system of equations by substitution.
y = 5x + 9y = −x + 3
Step: Solve = 5x + 9 for y:
y = 5x + 9
Step: Substitute 5x + 9 for y in y = −x + 3:
y = −x + 3
5x + 9 = −x + 3
5x + 9 + x = −x + 3 + x (Add x to both sides)
6x + 9 = 3
6x + 9 + −9 = 3 + −9 (Add -9 to both sides)
6x = −6
6x/ 6 = −6/6(Divide both sides by 6)
x = −1
Step: Substitute −1 for x in y = 5x + 9:
y = 5x + 9
y = (5)(−1) + 9
y = 4(Simplify both sides of the equation)
So our answers are y = -4 and x = -1.
