syms x

%

E = 207e9

%

d = piecewise( ...
    x < 0.04, 0.035, ...
    x < 0.1, 0.04, ...
    x < 0.21, 0.045, ...
    x < 0.275, 0.04, ...
    0.035)

%

I = pi * d^4 / 64

%

M = piecewise( ...
    x < 0.14, 3889 * x, ...
    980 - 3111 * x)

%

syms C1 C2
intrim = int( ...
    int( ...
        M / (E * I), ...
        x, 0, x) + C1, ...
    x, 0, x) + C2

%

sol = solve([ ...
    subs(intrim, x, 0) == 0, ...
    subs(intrim, x, 0.315) == 0])

%

y = subs(intrim, sol)

%

yp = diff(y, x)

%

disp(double(limit(yp, x, 0)))
disp(double(limit(yp, x, 0.14)))
disp(double(subs(yp, x, 0.315)))

%

fplot(y, [0, 0.315])

%

fplot(yp, [0, 0.315])