Question 441548
{{{ f(x) = x2 + 5x }}}
The derivative equation is
{{{ d1(x) = 2x + 5 }}}
{{{ d1(4) = 2*4 + 5 }}}
{{{ d1(4) = 13 }}}
and
{{{ f(4) = 4^2 + 5*4 }}}
{{{ f(4) = 16 + 20 }}}
{{{ f(4) = 36 }}}
Now I have a point, (4,36)
and the slope {{{ m = 13 }}}
{{{ y = mx + b }}}
{{{ y = 13x + b }}}
{{{ 36 = 13*4 + b }}}
{{{ 36 = 52 + b }}}
{{{ b = -16 }}}
The equation of the tangent is
{{{ y = 13x - 16 }}}
Here's the plot:
{{{ graph( 500, 500, -10, 6, -8, 44, 13x - 16, x^2 + 5x ) }}}