Calculating tangent lines

Function #f# is given by the function rule #f(x)= 2\cdot \euler^{x}+7\cdot x#. Let #k# be the tangent line to the graph of #f# at #x=2#.

How do we find the formula for #k#? Drag the steps of the solution into the correct order.

Calculate the derivative #f^{\prime}(x)#

#f(2) = 2\cdot \euler^2+14 #

Enter values of #\rv{x,y}# and #a# in #y=a \cdot x+ b#

#f^{\prime}(x) = 2\cdot \euler^{x}+7 #

Give the final formula for #k#

Calculate #b#, the #y#-intercept of the tangent

#a = f^{\prime}(2) = 2\cdot \euler^2+7#

Determine the slope #a# of the tangent

Find the #y#-coordinate of the point of tangency

#y = \left ( 2\cdot \euler^2+7 \right ) \cdot x -2\cdot \euler^2#

#b = -2\cdot \euler^2#

#2\cdot \euler^2+14 = \left ( 2\cdot \euler^2+7 \right ) \cdot 2 + b#