SOLUTION: A function whose tangent has slope 2x-3 for each value of x passes through the point(0,4).What is the minimum height of the graph

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Question 727922: A function whose tangent has slope 2x-3 for each value of x passes through the point(0,4).What is the minimum height of the graph
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
That tangent's slope is zero when
2x-3=0 --> 2x=3 --> x=3%2F2
For x%3C3%2F2 the tangent's slope is negative because 2x-3%3C0
and for x%3E3%2F2 the tangent's slope is positive because 2x-3%3E0 .
That means that the function decreases for x%3C3%2F2,
reaches its minimum value (minimum height of the graph) at highlight%28x=3%2F2%29
and increases for x%3E3%2F2.
There are infinite quadratic functions y=x%5E2-3x%2Bk whose tangent's slope is 2x-3 , but knowing that the graph passes through (0,4) we know that for x=0 {{y=k=4}}} so the function is
highlight%28y=x%5E2-3x%2B4%29
However, I do not know how you would know to start with y=x%5E2-3x%2Bk
because I never had to teach beginning calculus.