Question

The rate of photosynthesis R for a certain plant depends on the intensity of light x, in lumens, according to R(x)=180x−90x2.a. Sketch the graph of this function on a meaningful window.b. Determine the intensity x that gives the maximum rate of photosynthesis

Answer 1

we have the function

$R\mleft(x\mright)=180x-90x^2$

this is the equation of a vertical parabola open downward

the vertex is a maximum

step 1

Find out the vertex

using a graphing tool

see the attached figure

the vertex is the point (1,90)

therefore

Part a ------> option C

Part b -----> the intensity x is 1 lumen that gives 90 (maximum rate of photosynthesis)