A triangle has a height of 2x and a base of 7-4x. 1. What is the maximum area of the triangle? 2. What value of x gives the maximum area?

Question

campbell_st · Answer

well find the area $$A = \frac{1}{2} \times 2x \times (7 - x)$$. What do you get?

campbell_st · Answer

to find the maximum area. find the 1st derivative and then let it equal zero and solve for x. This will be the value of x that creates the maximum area.

campbell_st · Answer

the Alternate method, if you don't know calculus is graph the area curve. the highest point of the parabola is the max area.

campbell_st · Answer

you can graph the curve using https://www.desmos.com/calculator

campbell_st · Answer

another alternative is, once you have the Area equation. Find the line of symmetry, for a curve $$y = ax^2 + bx + c$$ the line of symmetry is $$x = \frac{-b}{2a}$$ then substitute thus value into the Area equation to find the max area

anonymous · Answer

if i simplify A=(1/2)(2x)(7−x) would i get 7x-4x^2 ? from that would i just complete the square to find the max?

campbell_st · Answer

no you can differentiate 

$$\frac{dA}{dx} = 7 - 8x$$

solve for x

x = 7/8

so the max area occurs when x = 7/8 units.... just substitute to find the area.