How to find the equation of the line tangent to the graph of f at the indicated value of x? f(x)= 4 - lnx ; x=1

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Answer 1 · 2017-02-13T16:56:20

#x+y=5#

#"we will use the equation: "y-y_1=m(x-x_1)#

#"where "(x_1,y_1)" is a known point on the line and " m= "the gradient of the line at that point"#

#" to find the gradient we need to calculate "f'(x_1)#

#f(x)=4-lnx#

#y_1=f(x_1)=f(1)=4-ln1=4-0=4#

#color(blue)((x_1,y_1)=(1,4))#

#f(x)=4-lnx=>f'(x)=-1/x#

#color(red)(m=f'(1)=-1/1=-1)#

#y-color(blue)(y_1)=color(red)(m)(x-color(blue)(x_1))#

#y-4=-1(x-1)#

#y-4=-x+1#

#x+y=5#