MATH 31A Midterm: Math 31A Exam 13
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1 f (x) = lim h 0 f (x + h) f (x) h. = lim a x f (a) f (x) tangent line at x = a y = f (a) + f (a)(x a) {z dx(cid:0) tan x(cid:1) = sec2 x d a x d dx(cid:0) cos x(cid:1) = sin x, Implicit derivatives d d dx(cid:0)xa(cid:1) = axa 1, dx(cid:0) sec x(cid:1) = sec x tan x, g(x)(cid:19) = d d d dx(cid:0) sin x(cid:1) = cos x, dx(cid:0) arctan x(cid:1) = f (x)g(x) f (x)g (x) d (cid:0)g(x)(cid:1)2. * take derivative of both sides w. r. t. x (don"t forget y terms) dx(cid:18) f (x) dx(cid:0)f (x)g(x)(cid:1) = f (x)g(x) + f (x)g (x) dx(cid:0)f(cid:0)g(x)(cid:1)(cid:1) = f (cid:0)g(x)(cid:1) g (x) F f (a) x or f (x) l(x) = f (a) + f (a)(x a) {z f > 0 f increasing f < 0 f decreasing f > 0 f concave up f < 0 f concave down.
