D is correct for (1)
For (2), the rule for differentiating x raised to some power is ' power down to the front, subtract 1 from the power '.
so ... ?
1) The derivative of f( x) at x = a can best be described graphically as:
A) Average value of the function, f( x), between x = 0 and x = a.
B) The slope of the line perpendicular to the graph of f (x) and containing the point (a,f(a)).
C) The slope of the line containing the two points (0, f(0) ) and (a, f (a)).
D) The slope of the tangent line to the graph of f (x) at the point (a, f(a) ).
I picked D for this one.
2) If f(x)= 8(sqrt x) + 6x^(3/4), find f '(x).
A) 4x^(1/2) + (9/2)x^1/4
B) 4x^(-1/2) + 8x^-1/4
C) 4(sqrt x) + (18/4)x^1/2
D) 4x^(-1/2) + (9/2)x^-1/4
Im really confused about this one. I would guess A, but not sure.