SOLUTION: A function H is differentiable at x =4. An equation for the line tangent to the graph of H at x=4 is 2x + 3y = 5. Find H(4) and H'(4). Please explain this. Thank you

Question 990405: A function H is differentiable at x =4. An equation for the line tangent to the graph of H at x=4 is 2x + 3y = 5. Find H(4) and H'(4).
Please explain this.
Thank you
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
2x + 3y = 5
solve for y
3y = -2x + 5
y = -2x/3 + 5/3
y = -2x/3 + 5/3
when x = 4
y = -2(4)/3 + 5/3 = -1
therefore we have a point of H(x) which is (4, -1)
H(4) = -1
*********************************************************
H'(x) is the slope of the tangent to H(x). It passes through (4, -1): that is the point at which it is tangent.
Remember that the equation of the tangent is
y = -2x/3 + 5/3
So the slope of the tangent line is -2/3. And it is H�(4), therefore
H'(4) = -2/3

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