SOLUTION: Hello, I am working through my application of derivatives assignment and have come across a question I kind of understand but am unsure if I should use my method, any help would be

Question 858241: Hello, I am working through my application of derivatives assignment and have come across a question I kind of understand but am unsure if I should use my method, any help would be highly appreciated:
The base b, and height, h, of a Triangle are represented by b= (t+3)^2 and
h= t^2+3. Determine the rate of change of the area of the triangle when t=3.
By my understanding, am I supposed to find b'(3) and t'(3)?
I do not understand how to fit in Area into this question
Any help would be much appreciated
Thank You
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we are given b= (t+3)^2 and h= t^2+3
Area of triangle is 1/2 * b * h
therefore
A = (1/2) * (t+3)^2 * (t^2+3)
A = (1/2) * (t^2+6t+9) * (t^2+3)
A = (1/2) * (t^4 + 6t^3 + 12t^2 + 18t + 27)
A = t^4/2 + 3t^3 + 6t^2 + 9t + 27/2
now
dA/dt = 2t^3 + 9t^2 + 12t + 9
for t = 3
dA/dt = 2*27 + 9*9 + 36 + 9 = 180

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