Find an equation of the tangent line to the given curve at the specified point. y...

  

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Find an equation of the tangent line to the given curve at the specified point. y = ex, (1, e) X Step 1 - To find the equation of a line with slope m through a point (xo, Yo), we can use y yo = m(x - xo). For y = f(x), the slope of the tangent line at (xo, Yo) is given by m = f'(xo). We have y = y' = ex. Therefore, we differentiate using the Quotient Rule. (x). et Step 2 Thus, the tangent slope at the point (1, e) is as follows. - (e¹). (1) m = f(1) = = (1) e = et (1) Suppose that f(2)= −5, g(2) = 2, f '(2) = −4, and g'(2) = 1. Find h'(2). (a) h(x) = 2f(x) - 4g(x) h'(2) = (b) h(x) = f(x)g(x) h'(2) = (c) h(x) = f(x) g(x) h'(2) = (d) h(x) h'(2)= = = g(x) 1 + f(x) Find an equation of the tangent line to the given curve at the specified point. y = ex, (1, e) X Step 1 - To find the equation of a line with slope m through a point (xo, Yo), we can use y yo = m(x - xo). For y = f(x), the slope of the tangent line at (xo, Yo) is given by m = f'(xo). We have y = y' = ex. Therefore, we differentiate using the Quotient Rule. (x). et Step 2 Thus, the tangent slope at the point (1, e) is as follows. - (e¹). (1) m = f(1) = = (1) e = et (1) Suppose that f(2)= −5, g(2) = 2, f '(2) = −4, and g'(2) = 1. Find h'(2). (a) h(x) = 2f(x) - 4g(x) h'(2) = (b) h(x) = f(x)g(x) h'(2) = (c) h(x) = f(x) g(x) h'(2) = (d) h(x) h'(2)= = = g(x) 1 + f(x)