document.write( "Question 1064333: if there is a function f and we know that f''(x)<>0 (f''(x) is not equal to 0) what does it mean for the f'(x) ?? (12th form student from Greece) \n" ); document.write( "

Algebra.Com's Answer #679439 by rothauserc(4718) $\"\"$ $\"About$

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f''(x) not = 0, tells us that f'(x) is increasing or decreasing
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\n" ); document.write( "1) f''(x) < 0, we know the slope of the tangent line (f'(x)) to f(x) is decreasing as x increases and we say that f(x) is concave down(graphically a parabola that curves downward)
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\n" ); document.write( "2) f''(x) > 0, we know the slope of the tangent line (f'(x)) to f(x) is increasing as x increases and we say that f(x) is concave upward(graphically a parabola that curves upward)
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