1) The limit equation to find the slope will look like this: f'(x) = limx→4[[f(x+4)-f(x)]÷4]. To find the slope at x=4 just plug 4 in the resulting equation. 2) The tangent line equation will look like this: y = f(4) + f'(4)(x-4) I hope this helps.
I'm assuming that the original function is x = √(y), is this correct? The only transformation is the multiplication by -1 giving the x = -√(y) equation. When multiplying by -1, you basically flip the graph about the axis that is not directly multiplied by the -1. It...
Using the quadratic equation: [-b ±√(b2-4ac)]/2a where a = 12, b = 10 and -3 = c.
For this equation, you would plug in x+9 everywhere you find the r in the original equation. What you get is 4/3*π(x+9)3. Expanding out the (x+9)3 term the equation comes to V= 4/3*π(x3+27x2+243x+729. Hope this helps. Correction made. Gotta...