Application of derivative
1. If , f(x)=4+3x-3x^2 find the equation of the line tangent to the curve f(x) at x=-5.
The tangent line is y= ?
2. A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 53 cm/sec. Find the rate at which the area within the circle is increasing after
(A) 2 seconds Rate of increase = ?
(B) 4 seconds Rate of increase = ?
(C) 5 seconds Rate of increase = ?
3. Let f(x)=-5x+7x^2. Then the expression f(x+h)-f(x)/h can be written in the form Ah+Bx+C, where A, B, and C are constants.
I found that A= 7 B= 14 C= -5
Use your answer from above to find the limit as h approaches 0 when f(x+h)-f(x)/h ??
Finally, find each of the following: f '(1), f' (2), f ' (3)
4. f(x)= sqrt(x+3)
f ' (5) ??
6. The slope of the tangent line to the curve y=3/x at the point (8,0.3750) is: ?
The equation of this tangent line can be written in the form y=mx+b where m is: ?
and where b is:?
I just started calc this week so feel free to bash me for my stupidity..