Let g(x)=ecx+f(x) and h(x)=ekxf(x), where f(0)=3,f(0)=5, and f(0)=2. a Find g(0) and g(0) in terms of c. b In terms of k find an equation of the tangent line to the graph of h at the point where x=0.
a) and in terms of .
b) Equation of tangent line to the graph of at .
a) implies . Also , then .
b) implies . You know that the slope of tangent line is . Therefore, is the point on the tangent line, when . Now you have a point on the tangent line and the slope of the tangent line. The only step left is to use the point and the slope in the point slope formula for a line. Therefore,
, i.e., , i.e.,. This is the equation for the tangent line in terms of .