Question

Determine the point at which the graph of the function has a horizontal tangent line. x2 f(x) x² + +4 (x, y) = Submit Answer

Answer 1

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Given To find: 223 Hence the point (x, y) at which the graph of function has f(x) = x2 x+4 . the point at which the graph of the functions has a horizontal tangent line. solution finding slope of tangent line - m= f'(x) (x²+4) (x²)'- x²(x²+4)' (x²+4)² m = f'(x) = (2+4) (2x) = x2(2x) (x²+4) 2 m= f(x) 2x3 + 82- (x²+4)2 m= f'(x) = 8x (x+4) Since tangent is horizontal ( Paralld to x-aris), then slope of horizontal tongent line (m)=o. therefore, y = f(x) = fco) 0²+4 m = 8x 0 (x+4) 8x = o x=0 0 Now, a horizontal tangent line is [ (x, y) = (0,0) (Any)